A jury found the defendant, Dwight John, guilty of murdering Lesmore Buffong in the first degree on theories of *330deliberate premeditation and felony-murder.1 On appeal, John argues that (1) his motion to suppress testimony he gave before a Federal grand jury and statements he made to an agent of the Federal Bureau of Investigation (FBI) should have been allowed because they were obtained pursuant to an immunity agreement; (2) the admission in evidence of John’s gang affiliation and gang-related activities was irrelevant and prejudicial; and (3) the trial judge erred in declining to conduct an individual voir dire of all the jurors after a single juror raised concerns about her safety on the first day of trial. After considering John’s arguments, and undertaking a complete review of the trial record pursuant to G. L. c. 278, § 33E, we affirm his conviction.
1. Background.
We recite the evidence in its light most favorable to the Commonwealth, reserving additional details for discussion in conjunction with the specific issues raised on appeal.
John was raised in a Brooklyn, New York, neighborhood where he became friends with George Chang, Dean Beckford, Sean Henry, and Winston Gordon. By the late 1980’s, these men had formed a gang, for which they adopted the name the “Poison Clan.”2 Under Chang’s leadership, the Poison Clan sold large amounts of crack cocaine in the Brooklyn area. Over time, dissension grew within its ranks, and on New Year’s Day, 1989, Chang was murdered by another member of the gang. After Chang’s death, the Poison Clan broke into two factions — one based in Virginia under Beckford’s leadership, and another based in Boston run by John, Henry, and Gordon.
The Boston-based Poison Clan operation distributed crack cocaine procured by Henry and sold by local youths, including Buffong. The operation was lucrative — bringing in about $10,000 a day — until Henry was murdered in New York in December, 1989. With Henry gone, the Boston arm of the Poison Clan lost its supplier and was forced to shut down. In 1990, John and Gordon returned to New York. Later that year, *331without John’s knowledge, Gordon returned to Boston to begin his own operation selling marijuana. Gordon hired Buffong as one of his dealers.
On December 14, 1990, John and a friend from New York, Tristin Palmer, visited Boston. Although they had no plans to meet him, John and Palmer accidentally encountered Gordon, who invited them to spend the night at his apartment. The next day, the men met Buffong, who was driving a black BMW motor vehicle. John commented on the quality of Buffong’s automobile,3 and when the men decided to go shopping, John rode with Buffong in the BMW. The others followed in two vehicles. Buffong purchased various articles of clothing, and when he paid for them, he displayed a large amount of cash to the group. On the way back to Gordon’s apartment, the vehicles became separated at a traffic light. Buffong and John, in Buffong’s BMW, made it through the light and disappeared. The others returned to Gordon’s apartment. About one-half hour later, John returned to the apartment alone, carrying Buffong’s automobile radio and keys. John said that he had taken Buffong to visit a friend and that he was going to pick him up later. John and Palmer subsequently left the apartment and returned without Buffong, but carrying the clothes he had purchased that day. When Gordon asked about Buffong, John showed him a nine millimeter handgun and said that Buffong “had to go .. . .He was asking me too many questions.”
Later that day, Boston police officers discovered Buffong’s body in an alley. He had been shot in the back of the head. On December 24, 1990, John was arrested in New York City. He was driving Buffong’s BMW; two guns — one of them a nine millimeter — were found in the car, together with Buffong’s wallet. John was not prosecuted for Buffong’s murder until many years later.4
At the trial, which took place in 2002, statements made by *332John to an FBI agent in 1997, confessing to Buffong’s murder, were admitted in evidence. Also admitted were excerpts of testimony given by John before a Federal grand jury in Virginia (investigating matters unrelated to the Buffong murder), describing the Poison Clan and his participation in its criminal activities.5
2. Discussion.
a. Suppression. John argues that the judge erred in denying his motion to suppress his Federal grand jury testimony and the statements he made to an FBI agent because they either were obtained under a grant of use immunity given him by a Federal prosecutor or were involuntary insofar as they were made under the reasonable belief that he had been given such immunity.
i. Immunity. In 1996, while he was awaiting trial on unrelated robbery charges in New York City, John contacted Arthur Storch, a high-ranking inspector in the New York City police department, with whom he had had a prior relationship. John told Storch that he had information regarding five gang-related homicides and that he would be willing to give this information to Storch, but did not want to be a witness and testify in court. In a series of interviews with members of the New York police department, John implicated Poison Clan members, including Beckford, in a wide range of criminal activity.6 The New York police shared this information with Assistant United States Attorney David Novak, who was building a Federal case in Virginia against Beckford and other Poison Clan members. *333Novak made arrangements for John to be brought to Virginia in the hope that he would agree to become a cooperating witness.
John’s interaction with the United States Attorney’s office while in Virginia is central to the disposition of his motion to suppress. At the evidentiary hearing on John’s motion to suppress, John and Novak gave differing accounts of their meetings and conversations.7 After the hearing, the judge made the following findings of fact.
When Novak and John first met, Novak advised John that he should be represented by local counsel, but John declined. Novak spent one-half hour attempting to persuade John to accept representation, but John was adamant. John also refused to sign a proffer letter prepared and presented to him by Novak that would have given him limited use immunity, and “emphatically stated that he wanted no deal; he just wanted to tell his story.” Novak believed that John’s willingness to cooperate in the Virginia investigation was not based on a desire to secure immunity or a plea bargain, but rather to “even the score” with Beckford, whom John believed to be responsible for Henry’s murder.8
John was then interviewed on a number of occasions by Federal agents, including Novak, without any promise of immunity. Subsequently, he testified before a Federal grand jury in Virginia about the Poison Clan’s members, its drug selling operations, and several gang-related murders.9 In exchange for John’s grand jury testimony, Novak promised that he would notify the Brooklyn, New York, district attorney of John’s cooperation in the Beckford investigation. This agreement was put on the record before the grand jury when John testified. The *334judge found that this was the only agreement between Novak and John.10
On the basis of John’s testimony and other evidence, Beck-ford and others were indicted on charges of racketeering, conspiracy, continuing criminal enterprise, and multiple homicides. As the Beckford trial approached, Novak learned that John, who remained incarcerated in Virginia, was acting strangely. When Novak visited him, John said that he would not testify at trial. Novak responded that John had no choice in the matter because, if necessary, Novak could strip him of his privilege under the Fifth Amendment to the United States Constitution by granting him immunity and compelling him to testify.
Thereafter, on May 21, 1997, shortly before the start of the Beckford trial, Novak filed notices with the court and defense counsel regarding both the criminal histories of prospective government witnesses and any rewards or inducements made in exchange for their testimony. With respect to John, the notice indicated that he had already received a more favorable plea bargain from the New York prosecutor, and stated that he “has been informed that he has use immunity for his statements, meaning that anything that he says cannot be held against him in any fashion.” The purpose of the notice was to ensure that defense counsel would be in a position effectively to cross-examine John (and other witnesses similarly situated) at trial. When viewed in the context of all of the conversations between John and Novak, the judge found this notice to mean that “if John testified at the [Beckford] trial in accordance with the prior grand jury testimony, he had use immunity for those statements” (emphasis in original).11 Because, as explained below, John did not testify at the Beckford trial, the judge further *335found that his statements and grand jury testimony were not protected by a grant of immunity.
On June 20, 1997, the Friday before John was scheduled to testify in the Beckford trial, FBI Special Agent Gerald Green, working with Novak, visited John to “take [his] temperature.” Green noticed that John seemed very agitated. He asked John whether the Beckford defendants knew something about him that the government did not, that might come up during his testimony at trial. John then told Green that he had killed Buffong. Green notified Novak of John’s confession and, not surprisingly, Novak decided not to call John as a witness. Green reported John’s confession to the Boston police, and John was reindicted for Buffong’s murder in 1998.
John argues on appeal that the judge’s findings of fact are clearly erroneous and not supported by the evidence. The issue here is strictly one of credibility — whose account of their meetings and conversations was more credible, Novak’s or John’s. If Novak’s testimony is believed, the judge’s findings are fully supported by the evidence. On questions of credibility, we will not substitute our judgment for that of the fact finder. Commonwealth v. Rivera, 424 Mass. 266, 269 (1997), cert. denied, 525 U.S. 934 (1998). There is nothing in the evidentiary record of this case that would cause us to vary from this rule. John’s statements and testimony were not obtained under a grant of immunity.
ii. Voluntariness. John argues that even if he was not immunized when he confessed to Green, his statement should nevertheless have been suppressed because it was given involuntarily.12 In essence, his argument is that his confession to *336Green was the “product of coercion resulting from [the] belief that he had been granted use immunity.”
The voluntariness of a confession turns on whether the defendant’s “will was overborne to the extent that [his] statements were not the result of a free and voluntary act.” Commonwealth v. Sneed, 440 Mass. 216, 222 (2003), citing Commonwealth v. Selby, 420 Mass. 656, 663 (1995). In denying John’s motion to suppress, the judge concluded that John was well acquainted with the interview process and his rights, was not under the influence of drugs or alcohol or affected by mental illness, and clearly had not been given immunity. Consequently, he found that his confession was given voluntarily. This finding is fully supported by the evidence, which also supports the judge’s implicit finding that John’s confession was made deliberately in order to avoid testifying at the Beckford trial.
Throughout his cooperation with the government, the evidence regarding John’s behavior was consistent with his stated desire to provide enough incriminating evidence against Beckford to “even the score” for Beckford’s involvement in Henry’s murder, but to avoid testifying. From the outset — even in his first contact with Storch — John expressed his desire to cooperate but not become a witness. When it became clear to John that Novak was going to seek to use him as a witness, he proceeded along a path intended to make himself as undesirable a witness as possible.
John first engaged in a pattern of bizarre behavior. He walked around the prison naked, threw feces, poured milk on his head, cut himself, banged his head against a wall, and tied a string around his neck in an apparent attempt to commit suicide. This behavior did not, however, deter Novak from his plan to use *337John as a witness.13 John next “dug in,” and directly told Novak that he would not testify at trial. Novak’s threat to strip him of his Fifth Amendment rights and force him to testify set the stage for John’s final act.
In what can only be understood as an apparent act of desperation, John did the one thing he believed would keep him off the witness stand: he confessed to murder. From prior (and repeated) questioning on whether he had ever killed anyone, it was apparent to John that Novak did not want to use cooperating witnesses who were themselves guilty of murder, and John’s confession had the desired effect of convincing Novak not to use him as a witness at the Beckford trial. In his personal calculus, John may have decided that facing a homicide prosecution was a better fate than incurring the wrath of the Poison Clan for testifying against them at trial. In any event, based on the record before him, the judge did not err in concluding that John’s confession was voluntary.
b. Gang evidence. John filed a motion in limine to exclude evidence of the New York activities of the Poison Clan. The judge denied the motion, and John objected to the admission of the evidence throughout the trial. He argues that it was error to admit the gang evidence because it was unnecessary and more prejudicial than probative.
This court has often held that gang affiliation evidence is admissible to show motive, and has given deference to trial judges’ determinations of the risk of unfair prejudice arising from such evidence. See Commonwealth v. Swafford, 441 Mass. 329, 332 (2004); Commonwealth v. Correa, 437 Mass. 197, 201 (2002); Commonwealth v. Maldonado, 429 Mass. 502, 504 (1999). Here, the judge determined that the evidence of the Poison Clan’s New York activities was relevant and necessary background to the murder. He also found that the evidence was not being offered for the purpose of demonstrating John’s propensity for criminality, and that it was not more prejudicial *338than probative.14 There was neither abuse of discretion nor any other error of law in the judge’s decision to admit this evidence. See Commonwealth v. Swafford, supra at 333; Commonwealth v. Smiley, 431 Mass. 477, 484 (2000).
In addition, beginning with their selection, the judge took steps to ensure that the jury would not misuse the evidence regarding the Poison Clan. During voir dire, the judge advised prospective jurors that “there may be evidence in this case that some of the people involved were or may have been involved or affiliated with a gang or gangs,” and inquired whether such evidence would interfere with the ability to render an impartial verdict. In his charge to the jury, the judge also gave a limiting instruction on the evidence as follows:
“There was evidence in the case that the defendant was a member of an organization that distributed drugs. Like all evidence, it is up to you to determine if it is true, and if it is, how much weight to give it in your deliberations on the charges in this case. But you should keep in mind the following: Mr. John is not on trial for drug distribution or for being a member of the Poison Clan. He’s on trial for the murder of Lesmore Buffong and for possession of a firearm on that date, December 15, 1990, the date alleged in the indictment. The evidence concerning the Poison Clan organization may provide you with background information about some of the participants in the events and the circumstances under which certain things happened or events transpired. But it would be improper . . . for you to conclude that Mr. John committed the crimes for which he is charged in this case merely because he was a member of the Poison Clan.”
This instruction and the voir dire questioning that preceded it satisfactorily fulfilled the judge’s responsibility to minimize the prejudicial effect that gang evidence might have had on the jury. See Commonwealth v. Correa, supra at 201; Commonwealth v. Maldonado, supra at 505 (voir dire and limiting instruction were adequate to minimize prejudicial impact of *339gang evidence). We will not disturb the judge’s determinations regarding the admissibility and handling of evidence of the Poison Clan’s New York activities.
c. Voir dire. At the close of the first day of the trial, after opening statements had been made by the parties, the judge received the following note from a juror: “Guns, drugs, gangs, murder. Should I have any reason to be worried about my own safety as a juror?” After consulting with counsel, and before the trial resumed the next day, the judge questioned the juror regarding the note. The judge told the juror that her concerns were not uncommon, but in his thirty years as a judge and a lawyer, he had never known of a juror being harmed in any way. The juror told the judge that she was reassured, and she agreed that she would be able to “keep an open and impartial mind and decide the case based on the evidence and no more.” When asked whether she had discussed her concerns with anyone, the juror said that she told another juror that she had written a note to the judge and the other juror responded, “Oh,” but they did not discuss it further. She stated that she had no other communication with anyone else regarding her concerns, nor had she heard any other jurors discussing the matter.
Defense counsel then moved that the juror be removed and that the judge conduct a voir dire of all of the jurors to ensure that they had not discussed the contents of the juror’s note. The judge denied the motion, and stated that he would continue his usual practice of admonishing jurors throughout the trial to refrain from discussing the case with one another. On appeal, John argues that denial of the motion for voir dire was an error requiring the reversal of his conviction.
Whenever a claim of extraneous influence on the jury arises, the trial judge should determine, within his discretion, whether there exists “a serious question of possible prejudice.” Commonwealth v. Tennison, 440 Mass. 553, 557 (2003), quoting Commonwealth v. Jackson, 376 Mass. 790, 800 (1978). If the judge determines such a question exists, he should conduct a voir dire of the jurors. Commonwealth v. Tennison, supra. In this case, the judge determined, after speaking with the juror who authored the note, that there was no serious question of *340possible prejudice.15 The judge’s determination that the juror’s concerns had been assuaged, and that she had given careful thought to her ability to remain impartial, was reasonable. See Commonwealth v. Gregory, 401 Mass. 437, 444 (1988) (“judge may properly rely on a juror’s statement that [she] remains impartial”).
It was also reasonable for the judge to determine that further voir dire was unnecessary where the juror had told only one other juror that she had written the note, but had not discussed its contents. See Commonwealth v. Francis, 432 Mass. 353, 370 (2000) (declining to disturb judge’s refusal to conduct individual voir dire of all jurors after single juror excused for expressing fear of harassment from gang members). See also Commonwealth v. Mendes, 441 Mass. 459, 477 (judge did not abuse discretion in declining to investigate juror’s claims of another juror’s bias); Commonwealth v. Tennison, supra at 560 (deferring to judge’s determination that second voir dire of all jurors unnecessary after single juror dismissed for communicating with defendant). Had the judge conducted the voir dire requested by John, he risked creating a question of possible prejudice by causing concern among the jurors where there was none. See Commonwealth v. Francis, supra at 370. The judge did not abuse his discretion by denying John’s request for a voir dire of the jurors.
d. G. L. c. 278, 33E. We have reviewed the entire record pursuant to G. L. c. 278, 33E, and we find no reason to exercise our authority to reduce the jury’s verdict or to order a new trial.
Judgment affirmed.
The defendant was acquitted on the charge of possessing a firearm without a license, in violation of G. L. c. 269, 10 (a).
The gang’s name is a reference to a “Kung-Fu” film called “Five Deadly Venoms.” The name was chosen because, as in the film, the gang’s members were “killing their own.”
At the time, John did not own a motor vehicle.
The arresting New York police officer testified that he had received a report of a suspicious vehicle. When he checked the registration plates, he learned that the vehicle was wanted in connection with a Boston homicide. John was apparently prosecuted in New York for weapons charges related to the firearms found in the BMW, and served a prison sentence. In 1994, Boston police officers went to New York to serve an arrest warrant on John for the *332murder of Buffong, but due to insufficient evidence available at that time, the charge was subsequently nolle pressed by the Suffolk County district attorney’s office.
The Commonwealth’s evidence also included Gordon’s testimony that John confessed the murder to him, a letter John wrote to a New York police inspector in 2000 asking why Palmer was also being held since “he had nothing to do with it,” and a letter John wrote to the Suffolk County district attorney in 1999 stating, “I am willing to make a confession dealing with the charges that are brought against me. I did the crime, however, I still need your help. I wait desperately for your response and actions.”
John initiated his communications with the New York police and there is nothing in the record to indicate he received any consideration in exchange for the information he provided to them. Storch testified that John “didn’t really ask for anything. He said — he gave me the information and he said, ‘I just don’t want to testify, but I want to give you the information.’ ”
In addition to Novak’s testimony, the judge also had before him John’s affidavit submitted in support of the motion to suppress.
In his affidavit, John claimed that Novak did not offer to provide him with an attorney, and that he did not sign the proffer letter because he believed that he already had been granted immunity as a part of his transfer to Virginia. John averred that he was confused as to why Novak would offer to immunize him again when he was already protected. The judge rejected this version of events.
The subject of Buffong’s murder did not come up during John’s grand jury testimony or the interviews that had preceded it. During Novak’s interviews, John was asked on more than one occasion whether he had ever killed anyone, to which he uniformly replied in the negative.
After John testified before the Federal grand jury, Novak did in fact inform the district attorney of John’s cooperation, and the district attorney reduced his plea offer on John’s New York robbery case from five to ten years down to from three to six years. John accepted the offer and pleaded guilty.
John suggests that the May 21 notice speaks for itself and establishes a broad grant of immunity, and he emphasizes that the May 21 notice is the only documentary evidence on the subject of any immunity. John’s argument that he relied on the broad statement of immunity in the May 21 notice is, however, disingenuous. John was never provided with a copy of the May 21 notice. Therefore, the only basis John would have for believing that he was im*335munized was whatever he gleaned from his conversations with Novak, and the judge ruled that a reasonable person could not conclude from those conversations that he had been immunized.
As a preliminary matter, we reject John’s argument that Green was required to provide him with Miranda warnings prior to the June, 1997, interview that yielded the admission. “Miranda warnings are only necessary where one is the subject of ‘custody and official interrogation.’ ” Commonwealth v. Larkin, 429 Mass. 426, 432 (1999), quoting Illinois v. Perkins, 496 U.S. 292, 297 (1990). The mere fact that an inmate is incarcerated does not require a finding that he is “in custody” for Miranda purposes. Rather, the question is “whether the prisoner would reasonably believe himself to be in *336custody beyond that imposed by the confines of ordinary prison life.” Commonwealth v. Larkin, supra at 435, quoting People v. Margolies, 125 Misc. 2d 1033, 1041 (N.Y. Sup. Ct. 1984). The defendant bears the burden of proving, in the totality of the circumstances, that he was “in custody.” Commonwealth v. Larkin, supra at 432, 435. John has failed to meet this burden. The judge correctly found that “[tjhere was nothing about the June 20 interview that would have suggested to John or any reasonable person that he was not free to leave, i.e., return to his cell in the Virginia jail in which he was then housed.”
As the judge noted, there was evidence that John was “malingering [or] feigning his symptoms to advance his own agenda.”
John’s Federal grand jury testimony, which was read into the record by the Commonwealth, was redacted to sanitize it of any testimony implicating John in any violent acts of the Poison Clan. The only evidence of John’s violence presented at trial was the murder of Buffong.
There was no evidence that the juror’s concerns arose from anything other than what she heard from counsel, in court, on the first day of the trial.