On December 15, 2003, a jury in Superior Court found the defendant, James Doyle, guilty of having trafficked in *847cocaine in an amount greater than fourteen grams but less than twenty-eight grams on July 8, 1999.1 On January 9, 2004, the defendant filed a motion for a new trial, which the motion judge (who was also the trial judge) denied without a hearing on May 20, 2005. The defendant, who relied on an entrapment defense at trial, here contends (appealing both his conviction and the denial of his motion for a new trial) that the judge should have granted him a new trial on the grounds that she had erred at trial by (1) refusing to direct a verdict of not guilty because the Commonwealth failed to present sufficient evidence to prove that he was predisposed to commit the crime charged beyond a reasonable doubt; (2) refusing to give a requested jury instruction on the role of a government informant in an entrapment case; (3) refusing to admit the government informant’s hearsay statement concerning his motive to work for the Federal Bureau of Investigation (FBI); and (4) refusing to permit the admission of evidence concerning the circumstances of the government informant’s death. We affirm the denial of the defendant’s motion for a new trial as well as the judgment.
Background. The jury could have permissibly found the following pertinent facts favorable to the Commonwealth.2 In 1999, State Trooper Thomas Nartowicz was assigned, in an undercover capacity, to an FBI task force that was investigating local motorcycle clubs suspected of selling narcotics. The task force used a cooperating informant named William Donáis to introduce Nartowicz to members of the Longriders Motorcycle Club (Longriders Club) in Ludlow. Donáis had previously infiltrated the Longriders Club for the task force, in January, 1998, to determine whether illegal drugs were being sold there. At trial, it was established that Donáis had agreed to cooperate with the authorities after being arrested for a traffic incident.3 The government paid Donáis in excess of $100,000 for his *848work over a period of several years (through early 2001), and he received other benefits, including housing and a motor vehicle.* 4
During the course of the investigation, Donáis introduced Nartowicz to the defendant, who was a former president of the Longriders Club. Shortly thereafter, on June 4, 1999, Nartowicz attempted to arrange a $500 purchase of cocaine from the defendant at the Longriders Club’s clubhouse, using Donáis as an intermediary.5 Although the defendant was unable to obtain cocaine at that time, he directed Nartowicz (but not Donáis) to join him in the clubhouse’s bathroom. There, after locking the door, he gave Nartowicz his money back and chastised him for not giving the defendant more time to procure the cocaine. The defendant also informed Nartowicz that he did not do business over the telephone, and that if anyone refers to anything (which Nartowicz understood to mean cocaine) over the telephone, he hangs up. The defendant assured Nartowicz, however, that he could probably obtain “something” (which Nartowicz again took to mean cocaine) to sell to him later that same night. Nar-towicz declined the offer on the ground that he could not wait around at that time, but said that he might contact the defendant through Donáis in the future.
On July 8, 1999, Nartowicz again met Donáis and the defendant at the Longriders Club’s clubhouse to buy cocaine. After securing the premises, the defendant asked Nartowicz for $650 as the price for his cocaine. When Nartowicz protested the increased price, the defendant explained that the price for the cocaine was higher “because he was getting it from a different guy now; and that the . . . other guy was in jail and they [the *849police] were attempting to deport him.” After Nartowicz paid the defendant the $650, the defendant told Nartowicz that he was meeting his new cocaine supplier at 8:30 p.m., and that Nar-towicz could meet him later to receive the “stuff” at Christy’s bar in Springfield.
Later that night, Nartowicz went alone to Christy’s bar and waited for the defendant. The defendant eventually arrived, sat down next to Nartowicz and, with a smile, told him that he “was going to like the stuff that he [the defendant] had,” referring to the cocaine. After finishing a beer, the defendant said he was “ready” and directed Nartowicz outside, where the defendant deposited the cocaine, wrapped in a package, into Nartowicz’s saddlebag on the side of his motorcycle.6 The defendant cautioned Nartowicz to drive carefully with the “stuff” and told Nartowicz that they could make the transaction a “weekly thing.” Nartowicz responded that he hoped the price would be reduced if they did arrange for a weekly purchase. The defendant then remarked that “the price fluctuates.” Donáis was not present at Christy’s that night. (At trial, Nartowicz identified the package he had received from the defendant, which he had turned over to a fellow officer soon after receiving it for laboratory analysis; the analysis disclosed the powder in the package to be seventeen percent cocaine).
On October 9, 1999, Nartowicz attended a social event sponsored by the Longriders Club at the American Legion hall in Chicopee. Again, Donáis was not present. The defendant approached Nartowicz and asked where he had been lately. After Nartowicz responded that he had been “around,” the defendant replied, “I thought we were going to do more business” (referring to the July 8 cocaine sale, the only “business” Nartowicz had ever conducted with the defendant). Nartowicz did not converse or interact further with the defendant thereafter. The defendant was indicted on September 27, 2001, for the July 8, 1999, sale of cocaine to Nartowicz.
At trial, the defendant relied on an entrapment defense, arguing that the government, through its agent, Donáis, had induced him to sell cocaine. He contended that he had undergone *850rehabilitation for a cocaine addiction in 1997 and was no longer addicted or predisposed to use or sell cocaine at the time that the government, through Donáis, infiltrated the Longriders Club in January, 1998. The defense offered numerous witnesses (all friends and associates of the defendant) who testified about Donáis’s persistent attempts to persuade the defendant to use and procure cocaine and about Donáis’s “intimidating [physical] appearance.”7 The defense also presented evidence that Donáis was a cocaine addict. However, the judge refused to admit evidence showing that the cause of Donáis’s death in 2003 resulted from an overdose of cocaine.8
Discussion. Entrapment. The defendant principally argues that his new trial motion should have been allowed because the judge erred in refusing to direct a verdict in his favor, where the Commonwealth allegedly failed to prove his predisposition to engage in cocaine trafficking beyond a reasonable doubt prior to his interaction with a government agent. In other words, he contends that his entrapment defense should have succeeded as matter of law because the Commonwealth failed to prove that he possessed the requisite criminal intent to sell drugs independent of the government’s inducement. He relies on the established proposition that entrapment occurs “when the criminal design originates with the officials of the Government, and they implant in the mind of an innocent person the disposition to commit the alleged offense and induce its commission in order that they may prosecute.” Sorrells v. United States, 287 U.S. 435, 442 (1932).
In order for an entrapment defense to be raised, evidence of inducement by a government agent must be presented at trial. Commonwealth v. Koulouris, 406 Mass. 281, 284 (1989). “Mere evidence of solicitation is not enough to show inducement,” *851ibid., quoting from Commonwealth v. Miller, 361 Mass. 644, 651-652 (1972), and, as the Supreme Judicial Court has noted, “[a]rtifice and stratagem may be employed [by the government] to bring to book those engaged in crime.” Commonwealth v. Harvard, 356 Mass. 452, 459 (1969), citing Sorrells v. United States, supra at 441. See Commonwealth v. Colon, 33 Mass. App. Ct. 304, 306 (1992) (“It is not unlawful for the government to set out bait for someone who takes the lure with alacrity”). The defendant did, however, offer sufficient evidence to meet the low threshold entitling him to an instruction on entrapment simply by testifying that Donáis, a government agent, induced him to sell the drugs to Nartowicz. See Commonwealth v. Miller, 361 Mass. at 651-652.9
Once an entrapment defense is adequately raised, the prosecution is required to prove beyond a reasonable doubt that the defendant was already predisposed to commit the crime. See Mathews v. United States, 485 U.S. 58, 62-63 (1988); Commonwealth v. Miller, 361 Mass, at 652; Commonwealth v. Thompson, 382 Mass. 379, 383-386 (1981); Commonwealth v. Shuman, 391 Mass. 345, 351 (1984). The central inquiry then becomes, “[W]as the defendant, initially not ready or willing to break the law, enticed or ensnared by the Commonwealth into overcoming his reluctance or resistance and doing so? Or did the Commonwealth merely provide the defendant, already ready and willing — already ‘predisposed’ — to commit the crime, an opportunity to do so?” Commonwealth v. LaBonte, 25 Mass. App. Ct. 190, 194 (1987). Predisposition may thus be found upon proof that “the accused [was] ready and willing to commit the crime whenever the opportunity might be afforded,” Commonwealth v. Miller, 361 Mass. at 651, quoting from United States v. Groessel, 440 F.2d 602, 605 (5th Cir.), cert. denied, *852403 U.S. 933 (1971), and the finding can be based upon the “[words and] conduct of the defendant as related to the indictment at issue [during his meetings with the undercover officer] ... if the evidence is of sufficient significance.” Id. at 652.10
The Commonwealth’s evidence — particularly that which exposed the defendant’s manifested willingness to engage in a drug transaction on June 4, 1999, and admitted ability to obtain drugs on short notice at that time — if believed, negated any rational inference that when the defendant sold the cocaine to Nartowicz on July 8, 1999, he lacked predisposition because he was “an innocent party . . . beguile[d] . . . into committing crimes which he otherwise would not have attempted,” Sherman v. United States, 356 U.S. 369, 376 (1958); or “that he acted out of fear,” Commonwealth v. Tracey, 416 Mass. 528, 537 (1993); or that he acted only in response to “[the informant’s] presumed suffering” or other importuning by the informant that “play[ed] on sympathy or other emotion,” Commonwealth v. Thompson, 382 Mass, at 385 (quotations omitted); or that he was subject to inducements that were “shocking or offensive per se,” or was effectively “corrupted” by the government’s undercover activities, Commonwealth v. Harvard, 356 Mass. at 460, quoting from Waker v. United States, 344 F.2d 795, 796 (1st Cir. 1965); or that he was enmeshed by “methods so outrageous or wicked as to deny him due process,” Commonwealth v. LaBonte, 25 Mass. App. Ct. at 195; or that he was reluctantly “persuade[d] ... ‘to turn from a righteous path to an iniquitous one.’ ” United States v. Gifford, 17 F.3d 462, 468 (1st Cir. 1994), quoting from United States v. Coady, 809 F.2d 119, 122 (1st Cir. 1987).
Moreover, the jury were not required to believe the “very feeble” (Commonwealth v. LaBonte, 25 Mass. App. Ct. at 195) *853defense version of events11 regarding the defendant’s purported lack of predisposition12 to sell drugs on July 8, 1999, and were entitled to discredit any or all of the defendant’s and his witnesses’ testimony to the effect that (a) Donáis readdicted the defendant around October, 1998, by providing him with cocaine and joining him in its consumption; (b) Donáis thereafter persisted in frequently asking, even imploring, him to procure cocaine for them to share, which the defendant adamantly refused to do (on one occasion vociferously and publicly) until June 4, 1999, when he reluctantly agreed to do so with $100 of his own money and $35 from Donáis; (c) the defendant could find no cocaine to buy that evening and tried to return Donáis’s money in the clubhouse bathroom, where he found Nartowicz (going under the alias “Vinny”), who claimed that it was his, and not Donáis’s, money and whose request that the defendant still try to obtain some cocaine that night the defendant firmly rejected; (d) the defendant at no time agreed with “Vinny” or Donáis to purchase cocaine for or sell cocaine to “Vinny”; (e) on July 8, 1999, after again reluctantly agreeing with Donáis to try to procure cocaine, with $500 of his own money, in order to share it with Donáis, and after finding some at a certain person’s home, the defendant went to Christy’s bar to meet Donáis but instead encountered “Vinny,” whose loud and boisterous demand that he turn over the drugs “spooked,” “scared,” and “panicked” the defendant, who precipitously took “Vinny’s” offered money, “threw the stuff in his [“Vin-ny’s”] [saddlejbag and . . . took off” because he “felt under the gun.”13
The prosecution, for its part, presented compelling evidence *854of the defendant’s predisposition to commit the crime charged, when viewed (as the judge was obliged to do in acting on the defendant’s motions for required findings of not guilty) in the light most favorable to the Commonwealth. See Commonwealth v. Monteagudo, 427 Mass. 484, 488 (1998). His exchanges with Nartowicz on June 4, 1999, and July 8, 1999, demonstrated a level of drug dealing experience, ability, sophistication, and eagerness that contradicted any impression that the government had corrupted an “innocent mind.” Massachusetts courts have recognized a variety of activities and characteristics as being strong evidence of a narcotics defendant’s predisposition, including the ability to procure illegal drugs for sale on short notice (see Commonwealth v. LaBonte, 25 Mass. App. Ct. at 194; Commonwealth v. Gratereaux, 49 Mass. App. Ct. 1, 3 [2000]; Commonwealth v. Remedor, 52 Mass. App. Ct. 694, 704 [2001]); familiarity with the terms of the drug trade and with market conditions in that trade (see Commonwealth v. LaBonte, supra; Commonwealth v. Gratereaux, supra; Commonwealth v. Remedor, supra); haggling over the price of illegal drugs (see Commonwealth v. LaBonte, supra at 191, 194; Commonwealth v. Colon, 33 Mass. App. Ct. at 306); discussion of having a continuing drug transaction relationship or future drug sales (see Commonwealth v. LaBonte, supra at 191; Commonwealth v. Colon, supra at 306; Commonwealth v. Gratereaux, supra); and committing the crime “readily and without reluctance,” see Commonwealth v. Monteagudo, supra; Commonwealth v. Remedor, supra. Here, the defendant manifested every one of those indicia of predisposition. As earlier noted, “[i]t is not unlawful for the government to set out bait for someone who takes the lure with alacrity.” Commonwealth v. Colon, supra.
Contrary to the defendant’s assertion that he was always reluctant and was effectively coerced into selling cocaine to Nartowicz, the prosecution’s evidence established (if believed) that at the time the police were investigating him, the defendant *855was already engaging in the drag business, took precautions to avoid police detection, and had already dealt with several sources of supply from which he could readily procure cocaine — powerful evidence that he was engaged in narcotics dealings with others that had nothing to do with the government. As Nartowicz testified, the defendant refused to discuss business over the telephone and was conversant with the fluctuating price of cocaine. Further, during the bathroom meeting with Nartowicz on June 4, 1999 — when the defendant took pains to lock the door and to exclude Donáis — the defendant made an offer, without the slightest solicitation, to obtain and sell Nar-towicz cocaine in the immediate future (since he had failed to procure cocaine earlier that evening), strong evidence of his enthusiastic predisposition. Finally, the defendant’s conduct during the July 8, 1999, transaction — refusing to negotiate a lower price (thus reflecting a purpose to maximize his profit from the transaction), offering to make regular, “weekly” cocaine sales to Nartowicz, and continuing to present the demeanor of one in complete charge of the drag deal — was uniformly inconsistent with his feeble story of either acting out of a desperate effort to avoid pressure from Donáis or having his will so dominated that he could not help himself.14
When considering a claim that the prosecution has failed to prove lack of predisposition beyond a reasonable doubt, the court must view the evidence in the light most favorable to the Commonwealth in order to determine whether a rational jury could have returned a guilty verdict. See Commonwealth v. Monteagudo, 427 Mass, at 488, citing Commonwealth v. James, 424 Mass. 770, 784-785 (1997). See also Commonwealth v. Colon, 33 Mass. App. Ct. at 306. Here, it is clear to us that a rational jury could have credited the Commonwealth’s evidence *856as amply sufficient to find the defendant guilty of trafficking in cocaine on July 8, 1999, because that evidence overwhelmingly demonstrated his predisposition to commit the crime.
The defendant attempts to overcome this reality by reliance on a statement taken out of context from the distinguishable case of Jacobson v. United States, 503 U.S. 540, 549 (1992), which he claims established the supposed principle that the Commonwealth must prove beyond a reasonable doubt that “the defendant was disposed to commit the criminal act prior to first being approached by Government agents.” We are unpersuaded. The literalness that the defendant ascribes to those words was clearly modified by the Jacobson Court’s example and statement (made immediately after the quoted passage) that a defendant’s “ready commission of the criminal act,” after being offered the opportunity to sell drugs and accepting the offer, “amply demonstrates the defendant’s predisposition.” Id. at 549-550. That example is the very situation involved here, where the defendant not only enthusiastically accepted the chance to sell cocaine to a new customer, but spoke freely about his general practices in and knowledge of the drug trade, including taking the precaution of never doing business over telephones, doing business behind locked doors, and staying abreast of price fluctuations for cocaine, as well as having ready access to multiple drug suppliers. The Jacobson Court’s explicit endorsement of the Federal government’s investigatory guidelines for offering suspects an inducement to commit a crime similarly finds application here,15 and the radically differ*857ent facts in Jacobson further undercut the defendant’s attempted application of that case to his situation.16
Under the core teaching of Jacobson, the jury were free to *858disbelieve the defendant’s version of events and to adopt the Commonwealth’s evidence of his predisposition to commit the crime charged. Such an inference could be permissibly and readily drawn from the circumstances of the defendant’s attempted sale to Nartowicz on June 4, 1999, his “ready commission” of the actual cocaine transaction on July 8, 1999, his stated willingness to continue to make such sales on a weekly basis, and his seeking out Nartowicz on October 9, 1999, to express apparent surprise and regret that more cocaine transactions had not ensued between them.17 Viewing the evidence in the light most favorable to the Commonwealth, we see no error in the judge’s denial of the defendant’s motions for required findings of not guilty and for a new trial, to the extent they depended on his entrapment defense.
Jury instruction. A related but secondary contention is the defendant’s complaint that the judge erred in refusing to give his requested jury instruction on the role of government agents in entrapment cases, on the ground that the standard Massachusetts instruction as given the jury by the judge contained *859no provision on inducement by government informants. (It is, of course, settled law that a defendant is not entitled to have an instruction phrased in the exact language he requests so long as the charge, taken as a whole, adequately conveys to the jury the applicable legal requirements. See Commonwealth v. Riley, 433 Mass. 266, 271 [2001]).
The judge correctly instructed the jury in the words of the Superior Court Criminal Practice Jury Instructions § 3.4 (1999), as follows:
“The defendant contends that a government agent or someone acting at the agent’s discretion induced him into committing trafficking [sic] cocaine. There is nothing improper about the police setting traps, such as with undercover methods, to catch those who are already disposed towards committing a crime. However, the state cannot tolerate having its officers instigate crime by implanting criminal ideas in innocent minds. The issue is not whether the government agent brought about this particular offense, but rather, whether the government agent brought about this defendant’s predisposition to the crime. No entrapment exists if a person is ready and willing to commit a crime whenever the opportunity presents itself and a government agent merely provides the opportunity or facilities to do so.”18 (Emphasis added).
After the judge had completed her charge, defense counsel, without objecting to any part thereof, requested that the court “consider” a further instruction on the role of government informants in entrapment cases, specifically that “government inducement may be offered [through] a cooperating informant acting at the direction of a government agent.” The judge said that she thought her instruction as given was adequate, to which *860defense counsel responded, “Thank you.”19
Contrary to the defendant’s assertion on appeal, he did not make or preserve an objection to this portion of the judge’s charge. That fact, combined with his failure to present any arguments that the judge’s action constituted an abuse of discretion (see note 25, infra) or created a substantial risk of a miscarriage of justice, dooms his contention.20
In any event, the defendant’s stated concern — that the jury would have been so misled by the instruction as to focus solely on the conduct of the government officials and not on the conduct of the government informant, Donáis, in considering whether the criminal design had been implanted in the defendant’s mind — is implausible. The jury could not have failed to have been aware, from the defendant’s and his witnesses’ testimony as well as that of the drug task force officers, that Donáis was a government informant acting at police direction to facilitate Nartowicz’s introduction to and dealings with the defendant. Moreover, reasonable jurors could not have failed to understand from the judge’s instructions, as applied to the facts of the case, that the issue of entrapment was to be determined by reference to the conduct of either “a government agent or someone [i.e., Donáis] acting at the government agent’s discretion” (emphasis added) — clear guidance that was plainly stated by the judge at the beginning of the charge on entrapment.
Government informant’s hearsay statements. The defendant also argues that the judge erred in refusing to admit statements allegedly made by Donáis in 2000 to his then girlfriend, subsequent to the crime charged, explaining why he became a government informant. At trial, the defense had sought to offer *861testimony from Donáis’ girlfriend that Donáis had told her that he became associated with the FBI after a gun he had sold was implicated in a murder in Hartford, Connecticut, and that the FBI threatened to prosecute him for the crime if he did not cooperate with them.
Faced with a “rank hearsay” objection from the prosecutor, defense counsel argued to the judge (during voir dire on the subject) that the testimony was offered solely as nonhearsay proof of Donáis’s “desperate” state of mind, which motivated his unremitting efforts to entrap the defendant, rather than for the truth of the facts asserted. The judge nonetheless refused to admit the evidence on the grounds that it was both cumulative and irrelevant. The defendant has failed to assert, much less establish, any abuse of the judge’s broad discretion (see note 25, infra) in deciding whether evidence is relevant, see Commonwealth v. Young, 382 Mass. 448, 463 (1981); Commonwealth v. Tobin, 392 Mass. 604, 613 (1984), or cumulative. See Commonwealth v. Urrea, 443 Mass. 530, 544 (2005).21
Instead, the defendant presents us with an argument, not made below, that is essentially inconsistent with the rationale he proposed to the judge for admission of the girlfriend’s proffered statement. Relying on the Supreme Judicial Court’s holding in Ruszcyk v. Secretary of Pub. Safety, 401 Mass. 418 (1988), he now claims that the statement should have been permitted as a hearsay exception because it was a vicarious admission, a statement by an agent binding his principal (here, the Commonwealth) that demonstrated why Donáis went to such lengths to lure the defendant into committing the crime.
His effort is unavailing. A party who has made an objection to a judge’s ruling on an evidentiary matter at trial after specifi*862cally stating the ground therefor is not entitled to urge different grounds on appeal of the court’s overruling of the objection. See Commonwealth v. Tyree, 387 Mass. 191, 213 (1982), cert. denied, 459 U.S. 1175 (1983); Commonwealth v. Noeun Sok, 439 Mass. 428, 435 (2003); Commonwealth v. Seap Sa, 58 Mass. App. Ct. 420, 427 (2003).
Moreover, even were the defendant’s reliance on Ruszcyk properly before us, it is misplaced. In that case, the court abrogated the common-law rule excluding admissions of an agent against his principal unless the agent’s actual authority to make the statement was established. Ruszcyk v. Secretary of Pub. Safety, 401 Mass. at 422-423. Instead, the court allowed the introduction of such statements if there were evidence that making them was within the scope of the agent’s employment, subject to the trial judge’s discretion to exclude them if their probative value was substantially outweighed by the danger of unfair prejudice to the opposing party (to be determined on a case by case basis). Ibid. Here, the proffered testimony was not shown to relate to any matter within the scope of Donáis’s agency with the FBI, but rather addressed only the issue how the agency relationship had (allegedly) come about in the first place.22
Death of William Donáis. The defendant’s final claim on appeal is that the judge erred in refusing to admit evidence of *863Donáis’s death, allegedly from a cocaine overdose in October, 2003, which the defendant offered to prove by means of a certified copy of an autopsy report from the medical examiner in Jacksonville, Florida.23 The judge agreed with the Commonwealth that the circumstances of Donáis’s death were too remote to be probative and, in any event, were irrelevant to the trial issues.24
Again, the defendant essays no argument that the judge’s ruling constituted an abuse of her wide discretion to determine the relevance of evidence and whether it was too remote. See Commonwealth v. Tobin, 392 Mass. at 613; Commonwealth v. Freeman, 430 Mass. 111, 116 (1999). The exercise of such discretion is accorded substantial deference by appellate courts in the absence of a clear showing (not made here) of its abuse — a very heavy burden25 — or palpable error, i.e., a decision that clearly transcends “the outer bounds of . . . discretion.” Commonwealth v. Bonds, 445 Mass. 821, 835 (2006).26 We are persuaded that evidence of Donáis’s death — over four years *864after the date of the crime for which the defendant was indicted and two years after Donáis had ceased to be a government agent — had such an attenuated relation to the defendant’s trial as to justify the judge’s implicit conclusion that it had little, if any, rational tendency to prove a material issue in the case against the defendant.27 Cf. Commonwealth v. Santiago, 425 Mass. 491, 494-497 (1997) (judge abused discretion by permitting repeated references in prosecutor’s closing argument to victim’s pregnancy and birthday, and by permitting victim’s sister to testify about her hospital vigil prior to victim’s death, because they were not relevant to any issue in case).
Judgment affirmed.
Order denying defendant’s motion for new trial affirmed.
The trial judge sentenced the defendant to three years in State prison. The judge had initially imposed a longer sentence but reduced it after granting the defendant’s motion to revise and revoke the sentence.
See Commonwealth v. Latimore, 378 Mass. 671, 677-678 (1979); Commonwealth v. Conkey, 443 Mass. 60, 72 (2004). These facts are also drawn from the judge’s findings in her May 19, 2005, memorandum of decision and order on the defendant’s motion for a new trial.
The defendant countered that Donáis actually began working for the police *848after a gun that he had owned was implicated in a murder in Hartford, Connecticut. However, the judge refused to admit this alleged information, as it was based on unreliable and prejudicial hearsay that was both irrelevant and essentially cumulative. See discussion, infra.
Donais also received a motorcycle, which was necessary to maintain his role as a member of the Longriders Club.
Donais, having infiltrated the Longriders Club over a year earlier, was already a trusted club member at this time. Nartowicz testified that the defendant was not the sole focus of his or the task force’s investigations, which were also directed at other Longriders Club’s members, and that both he and Donáis purchased cocaine from others in transactions that had nothing to do with the defendant.
Nartowicz rode a motorcycle to maintain his cover as a prospective member of the Longriders Club.
Donais was described as “6’3 . . . 360 pounds.” The Commonwealth presented evidence that Donáis neither coerced nor intimidated the defendant, and the defendant’s own witnesses also testified to his uniform resistance to Donáis’s alleged efforts to persuade the defendant to obtain cocaine for Donáis until June, 1999. The defendant, himself, testified that Donáis simply “ask[ed]” him if he wanted cocaine or would buy cocaine (albeit whenever he would see Donáis), and admitted that on at least one occasion, he vigorously rebuffed Donáis’s solicitation to procure cocaine (“I chewed him out. I read him the riot act”).
At that time Donáis had relocated to Florida. See discussion, infra.
The defendant claimed that Donáis caused him to become re-addicted to cocaine after he had gone through drug rehabilitation for cocaine addiction, and then pressured him in June and July, 1999, to obtain cocaine in order to satisfy Donáis’s and his own alleged renewed addiction. He denied that he had ever agreed to sell anything to Nartowicz. This satisfied the minimal burden a defendant must meet in order to be entitled to an entrapment instruction, even when the evidence of inducement is insubstantial and self-serving, or even implausible. See Commonwealth v. Tracey, 416 Mass. 528, 536 (1993).
The government activities that the courts are typically presented with as entrapment-producing “inducements” — “ ‘lengthy negotiations ..., aggressive persuasion . . . , coercive encouragement . . . [or] repeated or persistent solicitations’ of the defendant,” Commonwealth v. Shuman, 391 Mass. at 352, quoting from Commonwealth v. Thompson, 382 Mass. at 385 — did not occur during the defendant’s dealing with Nartowicz, and even Donáis’s alleged “persistent solicitations” did not, until June, 1999, involve efforts to induce the defendant to sell cocaine to anyone, much less a government agent. See note 7, supra.
Entrapment, when properly raised, is a jury issue, as part of the jury’s function of determining guilt or innocence, see Sherman v. United States, 356 U.S. at 377; Commonwealth v. Shuman, 391 Mass. at 351, and the jury are the appropriate arbiters of credibility. See Commonwealth v. James, 424 Mass. 770, 785 (1997); Commonwealth v. Hanlon, 44 Mass. App. Ct. 810, 815 (1998).
Inducement and predisposition are separate, though interrelated and mutually dependent, prongs of the entrapment doctrine. See, e.g., United States v. Gendron, 18 F.3d 955, 960 (1st Cir.), cert. denied, 512 U.S. 1051 (1994); United States v. Poehlman, 217 F.3d 692, 698 (9th Cir. 2000).
When asked why he gave “Vinny” the “stuff” instead of simply telling him that he had none, the defendant could only answer, “I don’t know. I really *854don’t know. I can’t say.” Under the defendant’s own account, the evidence of inducement was extremely thin, particularly in light of the defendant’s status as a past president of the Longriders Club, who was in a position at all times to have Donáis disciplined for possessing, using, or trying to acquire cocaine in the clubhouse, acts which were allegedly serious violations of club policy.
Additional evidence of the defendant’s ongoing predisposition can be seen in the encounter between the defendant and Nartowicz at a Longriders Club’s social event in October, 1999 (where Donáis again was not present). The defendant sought out Nartowicz and asked him where he had been lately. The defendant remarked that he thought they “were going to be doing more business” after July 8, 1999 (which had been the only “business” the two had ever transacted), with what could be rationally inferred as surprise and regret that more cocaine sales had not transpired — an attitude consistent with the behavior of one selling drugs as a business, not a corrupted innocent whose will had been overcome.
The United States Supreme Court observed that its holding in Jacobson “in no way encroaches upon Government investigatory activities,” under guidelines that permitted such inducement where “(a) [Tjhere is a reasonable indication, based on information developed through informants or other means, that the subject is engaging, has engaged, or is likely to engage in illegal activity of a similar type; or (b) The opportunity for illegal activity has been structured so that there is reason for believing that persons drawn to the opportunity, or brought to it, are predisposed to engage in the contemplated illegal activity.” Jacobson v. United States, 503 U.S. at 549 n.2, quoting from Attorney General’s Guidelines on FBI Undercover Operations (Dec. 31, 1980), reprinted in S. Rep. No. 97-682, at 551 (1982). In accordance with the guidelines, the FBI task force in the instant case had accumulated information from a variety of sources that the defendant was distributing cocaine as a *857member of the Longriders Club prior to the incident here.
In connection with the task force’s investigatory efforts in this case, the defendant called FBI Special Agent Cliff Hedges, who testified on cross-examination that the task force had targeted the defendant as the result of an accumulation of reports, particularly from several members of another motorcycle club, which identified the defendant as the Longriders Club’s chief cocaine trafficker. The judge allowed Hedges’s testimony (without details as to his sources), on the approved reasoning that such background extrajudicial information explaining the state of police knowledge and how the defendant came to the authorities’ attention, if carefully circumscribed, may be admitted so long as it is not used for the truth of the statements that served as the basis of the police knowledge. The judge correctly cited Commonwealth v. Rosario, 430 Mass. 505, 508, 509 (1999), in her ruling. Her limiting instruction to the jury (which the defendant’s counsel explicitly requested and thanked the judge for) —■ specifying that the “information [reported by Hedges] is not given to you so you can consider it for its truth . . . [but] to explain why the agents began their investigation. It does not go to the predisposition or the state of mind of the defendant” — may be presumed to have been followed by the jury, see Commonwealth v. Hanlon, 44 Mass. App. Ct. 810, 822 (1998); Commonwealth v. Correia, 65 Mass. App. Ct. 27, 37 n.8 (2005), and to have rendered harmless the supposed prejudice that the defendant conclusorily asserts (contrary to Mass.R.A.P. 16[a][4], as amended, 367 Mass. 921 [1975]) was created by the testimony. See Commonwealth v. Hanlon, supra. The defendant has presented no coherent argument demonstrating either “palpable error” in (see Commonwealth v. Robertson, 408 Mass. 747, 750 [1990], quoting from Commonwealth v. Young, 382 Mass. 448, 463 [1981]) or the lack of an honest conscientious, intelligent basis for (see Commonwealth v. Jaime, 433 Mass. 575, 579 [2001]) the judge’s exercise of discretion in making the challenged ruling. See Commonwealth v. King, 387 Mass. 464,472 (1982). Finally, the defendant’s appellate objection to Hedges’s testimony based on Crawford v. Washington, 541 U.S. 36 (2004), similarly lacks substance and violates Mass.R.A.P. 16(a)(4), being grounded in an unsupported and entirely speculative contention that the reports about the defendant to Hedges and the task force investigators had to have been “testimonial” as the product of supposed police interrogation.
Jacobson v. United States, 503 U.S. at 550, involved a defendant as to whom the government initially had no information regarding illegal activities, who was the target of twenty-six months of repeated mailings and communications from government agents to induce him to purchase illegal materials (child pornography) through the mails, efforts which the Court describes as having “exerted substantial pressure on” the defendant to make the illegal purchases (id. at 552), and which amounted to the government’s “implant[ing] in the mind of an innocent person the disposition to commit the alleged offense” so that it could prosecute “an otherwise law-abiding citizen who, if left to his own devices, likely would have never run afoul of the law” *858(emphasis in original). Id. at 553-554, quoting from Sorrells v. United States, 287 U.S. at 442. The lesson of Jacobson is that the government can use undercover investigations to catch criminals but not to create them. No decision, Federal or State, since Jacobson has adopted the defendant’s interpretation of the prosecution’s burden in an entrapment case. Compare, e.g., United States v. Gifford, 17 F.3d at 469; United States v. Aibejeris, 28 F.3d 97, 99 (11th Cir. 1994); United States v. Byrd, 31 F.3d 1329, 1336 (5th Cir. 1994), cert denied, 514 U.S. 1052 (1995); United States v. Garcia, 182 F.3d 1165, 1169 (10th Cir. 1999), cert. denied, 528 U.S. 987 (1999); Commonwealth v. Monteagudo, 427 Mass. at 488. As these decisions illustrate, what is critical is not the date when a government agent first became involved with a suspect generally but when, through the agent, the government began specifically to “beguil[e] him into committing crime,” Jacobson v. United States, 503 U.S. at 553, quoting from Sherman v. United States, 356 U.S. at 376, which did not occur here until Nartowicz’s June 4, 1999, offer to buy cocaine, an “opportunity . . . [the defendant] promptly availed himself of.” Id. at 550." The jury were not obliged to credit the self-serving testimony of the defendant and his witnesses that Donáis, acting as a government agent, persistently cajoled him to use and sell cocaine prior to June, 1999. Indeed, the record is devoid of any evidence that Donáis had ever tried to induce the defendant to sell cocaine to anyone prior to June 4, 1999.
As earlier noted, predisposition may be found solely based on “the conduct of the defendant as related to the indictments at issue . . . if the evidence is of sufficient significance,” Commonwealth v. Miller, 361 Mass, at 652, which a jury could readily find had been presented by the prosecution in this case.
The word “discretion” as used in the model charge may be an inadvertent misprint, since the alternative Superior Court instruction on entrapment uses the more apt phrase, “someone acting under the direction ... of a government agent.” Superior Court Criminal Practice Jury Instructions § 3.5 (1999). See Commonwealth v. Tracey, 416 Mass. at 537 n.10 (“we have said that the defense of entrapment is raised by evidence of inducement by a government agent or one acting at his direction”) (emphasis in original).
In his written proposed instructions, the defendant had cited Commonwealth v. Rancourt, 399 Mass. 269, 274 (1987), in purported support of this charge. That case is of no help to him, however, since it had nothing to do with instructions or entrapment, but rather involved the issue whether a person could be characterized as a government agent simply because he was attempting to curry favor with law enforcement officials. The court held that he cannot be so characterized. Id. at 274-275.
See Commonwealth v. Barbosa, 399 Mass. 841, 844 (1987); Commonwealth v. Gordon, 407 Mass. 340, 350 (1990); Mass.R.A.P. 16(a)(4), as amended, 367 Mass. 921 (1975); Mass.R.Crim.P. 24(b), 378 Mass. 895 (1979).
The prosecutor had argued against the girlfriend’s testimony on the additional basis that, even if relevant, any minimal probative value was “tremendously outweighed ... by the prejudice” to the Commonwealth’s case from putting the subjects of a gun and a murder involving a government agent before the jury. The judge may have been alluding to this ground when she specifically warned defense counsel to admonish the girlfriend not to make any “reference to a gun in a murder in Hartford” in her testimony, and it would have been within her sound discretion to exclude the evidence on that ground as well. See Commonwealth v. Booker, 386 Mass. 466, 469-470 (1982).
Additionally, as noted in note 21, supra, the “tremendous” prejudicial impact of such evidence was raised by the prosecutor, and if the defense had sought to have the statement admitted as a hearsay exception, i.e., for the truth of the matter asserted, such prejudice would have justified its exclusion in the judge’s discretion under the Ruszcyk rationale. See Ruszcyk v. Secretary of Pub. Safety, 401 Mass. at 422-424. Cf. Commonwealth v. Martinez, 431 Mass. 168, 173-175 (2000) (testimony by defendant’s girlfriend, that defendant’s niece had threatened to kill her if she testified against him, was improperly admitted as its probative value was negligible and risk of prejudice was “significant”). Further, the factors mentioned by the court in Ruszcyk as relevant to the inquiry — “the credibility of the witness; the proponent’s need for the evidence. ... ; and the reliability of the evidence offered,” Ruszcyk v. Secretary of Pub. Safety, supra — all would weigh against the defendant here. The witness, who was an admitted long-time cocaine abuser, also admitted to being the defendant’s girlfriend, and to having felt betrayed by Donáis, who had concealed his status as a government informant from her. The evidence of Donáis’s motive for being a government informant was extensively spread upon the trial record through various witnesses. And the proffered statement was far from reliable, defense counsel himself having conceded during voir *863dire that its truth was irrelevant and the prosecutor having vigorously disputed the accuracy of the statement.
Donais had moved to Florida sometime in 2001 and ceased to have a cooperating role with the government soon thereafter.
The prosecutor had also objected to the autopsy report as hearsay. The defendant here argues that it should have been deemed authenticated as an official record, but he provides no decisional authority supporting that position, nor was any relevant authority on the point provided to the judge at the voir dire on the document. In addition, the autopsy report does not address whether Donáis ingested the cocaine by mistake, ruse, while incapacitated, or by force. The defense presented no evidence regarding the 2003 death on the issue whether Donáis possessed this cocaine knowingly or intentionally, further diminishing the probative value of the evidence.
“In order to find an abuse of discretion, ‘it is necessary to decide that no conscientious judge, acting intelligently, could honestly have taken the view expressed by [her].’ ” Commonwealth v. Anderson, 445 Mass. 195, 209 (2005), quoting from Commonwealth v. Jaime, 433 Mass. 575, 579 (2001). Alternatively, the appellate court would have to be persuaded that the trial judge’s action reflected “arbitrary determination, capricious disposition, whimsical thinking, or idiosyncratic choice.” Greenleaf v. Massachusetts Bay Transp. Authy., 22 Mass. App. Ct. 426, 429 (1986).
The “palpable error” analysis is most commonly applied to a trial judge’s discretionary balancing of the probative value of proffered evidence and its risk of unfair prejudice or jury confusion. See Commonwealth v. Rosario, 444 Mass. 550, 557 (2005); Commonwealth v. Bonds, 445 Mass. at 831. No case appears to have drawn any clear distinction, if one exists, between the contents *864of the abuse of discretion standard vis-a-vis the palpable error standard.
The defendant never demonstrates how this supposed evidence of Donais’s death from “cocaine toxicity” so long after the events at issue could have had a significant impact on the jury verdict. This is unsurprising, in light of the substantial trial evidence of Donais’s cocaine use during the relevant time period and the fact that the defendant himself testified that two years constituted sufficient time within which to develop a cocaine habit, go through rehabilitation, become sober and productive, then resuccumb to cocaine addiction.