The defendant was convicted of murder in the first degree on a theory of felony-murder, the predicate felony being attempted armed robbery. He also was convicted of carrying a firearm without a license. On appeal the defendant contends that the judge erred (1) by denying his motion to suppress evidence seized pursuant to a warrant that was based on observations made during an earlier warrantless entry of a college dormitory room where he had been staying; (2) by admitting evidence of his prior bad acts; (3) by denying his motion for a mistrial based on the Commonwealth’s response to his Bowden defense; and (4) by failing to instruct the jury that they could not convict him of felony-murder in the first degree based on the firearms conviction. We affirm the convictions and decline the request to grant relief under G. L. c. 278, § 33E.
1. Background. The jury could have found the following facts. We reserve other details for discussion of the issues.
During the fall of 2008 and spring of 2009, the defendant, who was from New York City, was a frequent overnight guest in the Lowell House dormitory room of his girl friend, Brittany Smith, a senior at Harvard University (Harvard). In May, 2009, he met the victim, a twenty-one year old Cambridge resident who regularly sold marijuana to Harvard students. On or about May 17 he devised a plan to rob the victim. He told the victim that he was a Harvard student and that he lived at Kirkland House. He said he wanted to buy three pounds of marijuana. The defendant arranged to have two friends from New York City, Blayn Jiggetts and Jason Aquino, bring a gun and help him with the robbery. Jiggetts and Aquino traveled by bus to South Station in Boston where the defendant met them on the afternoon of May 18. They brought a nine millimeter, semiautomatic pistol and ammunition.
*407Using Smith’s cellular telephone, the defendant arranged to have the victim bring the marijuana to a secluded art room in the basement of Kirkland House that had one means of ingress and egress. The plan called for Jiggetts to produce the gun at the moment of the exchange; the defendant would then grab the marijuana. When the four men arrived in the art room, Jiggetts pulled out the gun and demanded that the victim turn over the marijuana. The victim refused to surrender it. Jiggetts passed the gun to the defendant, then approached the victim. The victim fled.
The defendant fired three shots at the victim; one bullet struck him, but he continued to run. The defendant, Jiggetts, and Aquino pursued the victim as far as the entrance to the building, and then went to Lowell House to meet Smith, who was waiting with a bag packed for travel. The defendant briefly explained what happened. He gave Smith the gun and told her to hide it. She wrapped the gun in some clothing and hid it in the nearby dormitory room of a close friend. After the defendant said that they had to leave immediately, Smith, the defendant, Jiggetts, and Aquino took a taxicab ride to South Station, where they boarded a bus to New York City.
In the meantime, the victim collapsed on Dunster Street in Cambridge. He called to a pedestrian for help, saying he had been shot. He was taken by ambulance to a local hospital where he died from the gunshot wound. Police later found a bag of marijuana wrapped in a bloody shirt; the victim had dropped it in the course of his flight.
2. Motion to suppress. The defendant filed a motion to suppress a black and orange “letterman” or “varsity” style jacket seized from Smith’s dormitory room. Police and Harvard personnel had entered Smith’s room without a warrant to check on her well-being. They saw the jacket and returned later with a warrant for the jacket and seized it. The defendant asserted a reasonable expectation of privacy in the dormitory room, and argued that police did not satisfy the requirements of the emergency exception to the warrant requirement of the Fourth Amendment to the United States Constitution and art. 14 of the Massachusetts Declaration of Rights when they first entered Smith’s room.
A judge of the Superior Court, not the trial judge, held an *408evidentiary hearing on the defendant’s motion to suppress. She denied the motion. We summarize her findings of fact, which are not disputed. Witnesses told police they heard three loud bangs in the area, and then saw three black males running from Kirkland House. One of the males was wearing a black and orange “letterman” or “varsity” style jacket. Smith’s Harvard identification card had been “swiped” through electronic card reading devices at three locked doors at Kirkland House around the time of the shooting. No woman was among those seen fleeing Kirkland House at that time. Smith’s identification card was later swiped at Lowell House, where she resided. In addition, the victim’s cellular telephone showed that he had telephoned Smith’s cellular telephone shortly before the shooting.
A State police officer tried to contact Smith. He called her cellular telephone on May 18 and 19, but he received no answer and she did not return his call. He also knocked on her dormitory room door but received no response. Her dormitory room window was open and a light was on in her room. Students living in her dormitory had not seen her since the time of the shooting. The officer spoke with the dean of Lowell House, who expressed concern that the officer had been unable to make contact with Smith. The dean called Smith’s cellular telephone himself and left a message. Although the dean told the officer that Smith always returned his telephone calls promptly, she did not return his call.
In consideration of these circumstances, a Harvard police sergeant, consistent with university police practice, entered Smith’s dormitory room on May 19 to check on her well-being. Officers of the State and Cambridge police departments accompanied him. Smith was not present. They saw a black and orange jacket similar to the description given by witnesses. They left the room about forty-five seconds after entering and posted an officer outside Smith’s room while they applied for and obtained a search warrant for the jacket.
The defendant and the Commonwealth stipulated to certain facts, summarized as follows. The defendant stayed in Smith’s dormitory room sometimes for weeks at a time. There is no evidence he ever received permission from Harvard to stay there. He left Massachusetts on May 18, went to New York City, *409and did not return. On May 21, he was arrested for the murder in this case. The judge concluded that the defendant abandoned the dormitory room on May 18.
The parties also stipulated to Harvard’s written policies governing enrollment and residency, which are summarized in relevant part as follows. “A person not regularly assigned to a particular dormitory or House may not be lodged [therein] for more than a brief stay without the permission of the Proctor, Resident Dean, or House Master[, and t]he consent of other occupants of the room . . . .” Students must keep dormitory doors locked at all times, and never prop open doors or allow visitors to “piggy back” with them when entering their residence hall. “The University must have access to all student suites and the rooms within them.” “Unauthorized or inappropriate possession of any key or passkey ... is prohibited.”
The defendant argues that he had a reasonable expectation of privacy in Smith’s dormitory room because he was a long-term invited overnight guest of Smith, and that his “subjective expectation of privacy [is one that] society is willing to recognize . . . as reasonable.” Commonwealth v. Williams, 453 Mass. 203, 208 (2009), quoting Commonwealth v. Montanez, 410 Mass. 290, 301 (1991). The defendant relies on Minnesota v. Olson, 495 U.S. 91, 99 (1990), in which the United States Supreme Court held that a houseguest who is present with the permission of his host enjoys a reasonable expectation of privacy in the host’s home. Unlike the host in the Olsen case, Smith did not stand in the position of a host who has “ultimate control” of her dormitory room. Id. She did not have the authority to “admit or exclude from the [dormitory room] as [s]he prefer [red].” Id. Harvard’s dormitory policy prohibited Smith from allowing the defendant to live in her room for more than a “brief stay” without the permission of certain university officials. She had not obtained such permission for the defendant’s long-term occupancy. Moreover, the defendant’s use of Smith’s pass key (her university identification card) was both “unauthorized” and “prohibited” under Harvard’s written policies governing enrollment and residency.
The defendant’s assertion that society would be willing to recognize his expectation of privacy in Smith’s room as reason*410able because he lived in the room lacks support in both fact and law. His rights in the dormitory room were less than Smith’s rights in the room. Smith’s right to allow the defendant to live in her room for more than a brief stay depended on her securing permission from university officials, which she did not obtain. In addition, she had no right to allow the defendant to use her pass key to gain access to university property that was not accessible by the general public. Indeed, his use of the pass key was expressly prohibited by Harvard’s written policies. Where the owner of the premises, Harvard, specifically forbade the type of use and occupancy involved, the defendant may not claim that his subjective expectation of privacy was objectively reasonable. That is, he may not claim that his expectation of privacy was one that “society is willing to recognize ... as reasonable.” Commonwealth v. Williams, 453 Mass. at 208. We conclude that there is no support for the defendant’s claim that he had a reasonable expectation of privacy in Smith’s dormitory room. The judge did not err in so ruling.
The judge also did not err in determining that even if the defendant had a reasonable expectation of privacy in Smith’s dormitory room, he abandoned the premises when he left for New York City on May 18. Abandonment is a question of intent. See Commonwealth v. Paszko, 391 Mass. 164, 184-185 (1984). Witnesses described three men leaving Kirkland House at the time of the shooting. One description partially matched the defendant. His departure from Massachusetts was abrupt, and he manifested no intent to return to Massachusetts. See Commonwealth v. Mallory, 56 Mass. App. Ct. 153, 159 (2002). The judge’s determination of abandonment had ample support in the record.
The judge further determined that even if the defendant had a reasonable expectation of privacy in Smith’s room, the warrant-less entry by police was justified under the emergency aid exception to the warrant requirement. The emergency aid doctrine “permits the police to enter a home without a warrant when they have an objectively reasonable basis to believe that there may be someone inside who is injured or in imminent danger of physical harm.” Commonwealth v. Peters, 453 Mass. 818, 819 (2009). The defendant argues that the police lacked an objectively reason*411able basis for believing that someone inside Smith’s room was in need of immediate aid. See Michigan v. Fisher, 558 U.S. 45, 47 (2009); Commonwealth v. Entwistle, 463 Mass. 205, 213 (2012), cert. denied, 133 S. Ct. 945 (2013). We disagree.
The police knew that calls were exchanged between the victim’s cellular telephone and Smith’s cellular telephone shortly before the victim died. They also knew that Smith’s identification card had been used to open three locked doors at Kirkland House at about the time of the shooting, and that it was used shortly thereafter at Lowell House, where Smith resided. No one had seen Smith for nearly twenty-four hours since the time of the shooting. She did not respond to telephone calls or knocks on her door by police. The light was on in her room, and the window was open. She did not respond to the voice message from the dean of Lowell House, whose calls she customarily returned promptly. The dean was concerned about her well-being. The police had reason to believe there was some connection between Smith and the homicide, and they could not rule out that Smith also may have been a victim.
Although there was no way of knowing precisely whether Smith was in her dormitory room or whether she had been injured and was in need of aid, there was a reasonable basis to believe she was in her room, and “there was a reasonable basis to believe that something unfortunate might have happened that rendered [her] unable to communicate” with persons, including police, who were attempting to ascertain if she was injured or in danger. Commonwealth v. Entwistle, 463 Mass. at 216. On this record, the police were fully warranted in entering Smith’s dormitory room under the emergency aid doctrine. There was no error in denying the defendant’s motion to suppress evidence.
3. Prior bad act evidence. The defendant argues that the judge erred by admitting evidence that, six months before the shooting in this case, the defendant negotiated the purchase of a large quantity of marijuana from a drug dealer who sold drugs to students at Yale University. With help from Jiggetts, the defendant robbed the dealer at gunpoint in the hallway of an apartment building in New York City pursuant to a plan similar to the plan they devised to rob the victim in this case. The defendant contends that the prejudicial impact of this evidence *412far outweighed its probative value. He further contends that the judge failed to undertake on the record a balancing process in which he was required to consider whether the prior bad act evidence was necessary for the Commonwealth to prove its case.
“It is well settled that the prosecution may not introduce evidence that a defendant previously has misbehaved, indictably or not, for the purpose of showing his bad character or propensity to commit the crime charged, but such evidence may be admissible if relevant for some other purpose. . . . Such evidence can be highly prejudicial to the defendant, and therefore must be excluded unless it comes within one of the permitted uses, such as to show a common scheme, pattern of operation, absence of accident or mistake, identity, intent, or motive. . . . [The evidence] must be relevant to the offense charged; where the relevance is not substantial but borderline, the evidence must be excluded unless its probative value on the issue in contention outweighs the undue prejudice that may flow from it.” (Citations omitted.) Commonwealth v. Helfant, 398 Mass. 214, 224-225 (1986).
The defendant relies primarily on two cases for his argument that the judge must consider whether the prior act evidence was necessary for the Commonwealth to prove its case. The first is Commonwealth v. Jackson, 132 Mass. 16, 20-21 (1882). That case involved the admission of evidence of prior bad acts that were not sufficiently similar to the crime charged for purposes of showing the defendant in that case had the requisite intent to commit the crime charged. Id. at 17, 19-20. The court did not hold, or even suggest, that the Commonwealth must show that it needed the prior bad act evidence to prove its case.
The second case on which the defendant relies in support of his argument as to necessity is Old Chief v. United States, 519 U.S. 172, 182-183 (1997). That case did not involve a constitutional principle, but the proper application of Fed. R. Evid. 403. Id. at 180. It also did not involve prior bad act evidence in the same context under consideration here. Instead, it arose in the context of the question whether a judge abuses his discretion by rejecting a defendant’s offer to stipulate to his prior conviction of a felony, an element of a prosecution under 18 *413U.S.C. § 922(g)(1) (possession of firearm by anyone with prior felony conviction), where the prior felony conviction is for assault causing serious bodily injury and where the defendant was defending charges of using or carrying a firearm during the commission of a violent crime and assault by means of a dangerous weapon. Id. at 174-177. The prosecution refused to join in the stipulation, and the judge allowed the prosecution to introduce in evidence the defendant’s prior conviction, including the name of the prior offense. Id. at 175-177. The Supreme Court concluded that in the circumstances, allowing the prosecutor to place the name of the felony of which the defendant previously had been convicted rather than merely the fact of the prior felony conviction created prejudice that substantially outweighed the probative value of the evidence that was admitted. Id. at 185. It was in this context that the Court reasoned that the identity of the particular felony of which the defendant previously had been convicted was not “necessary.” Id. at 186.
Significant to our analysis is the Court’s statement limiting its holding. The Court said, “[wjhile our discussion has been general because of the general wording of Rule 403, our holding is limited to cases involving proof of felon status. On appellate review of a Rule 403 decision, a defendant must establish abuse of discretion, a standard that is not satisfied by a mere showing of some alternate means of proof that the prosecution in its broad discretion chose not to rely upon.” Id. at 183 n.7. The Court limited its “necessity” requirement to cases where proof of a prior bad act, specifically a prior felony conviction, is an element of the prosecution’s case. Id. Our jurisprudence has no requirement that the Commonwealth show “need” for evidence of prior bad act evidence. The only requirements are relevance and a showing that the probative value of the evidence outweighs its prejudicial impact. See Commonwealth v. Helfant, 398 Mass. at 224-225. We see no reason to change our jurisprudence. We hold that the Commonwealth was not required to show that it needed the prior bad act evidence to prove its case, and that the judge was not obligated to consider whether the Commonwealth needed the prior bad act evidence or whether there was some alternative means by which the Commonwealth could prove its case.
*414The evidence of the defendant’s prior bad act was not used for an impermissible purpose, i.e., propensity to commit crime or bad character. See id. at 224. Rather, it was offered to show modus operandi, the defendant’s intent, and the absence of mistake,1 permissible purposes for admitting such evidence. See id. See also Commonwealth v. Sullivan, 436 Mass. 799, 806 & n.6 (2002). The judge gave the jury limiting instructions concerning the proper use of such evidence during jury selection and four times during the trial, employing forceful terms. The jury are presumed to have followed the instruction. Commonwealth v. Helfant, supra at 228-229, and cases cited. The judge was aware of this issue early in the proceedings and monitored the development of the evidence closely in anticipation that such evidence eventually would be offered. He issued a written memorandum explaining his decision prior to admitting the testimony in evidence. Significantly, he permitted the Commonwealth to use only a highly abridged version of the prior bad act evidence.
We are satisfied that the prior bad act evidence was highly probative of the defendant’s intent, his modus operandi, and the absence of mistake, and that the judge carefully and properly exercised his discretion through the use of limiting instructions and limitations on the Commonwealth’s proof to ensure that such evidence was used by the jury only for permissible purposes, and to ensure that the evidence did not create unfair prejudice. There was no abuse of discretion.
4. Motion for mistrial. Trial counsel had cross-examined Detective John Crowley of the Cambridge police department about the thoroughness of the investigation, thus laying the basis for a Bowden defense. See Commonwealth v. Bowden, 379 Mass. 472, 486 (1980). See also Commonwealth v. Phinney, 446 Mass. 155, 165-166 (2006). On redirect examination the prosecutor asked Crowley if Aquino indicated during his interview with police whether anyone had admitted to being the shooter. The defendant objected, and the judge sustained the objection. The defendant moved for a mistrial, which the judge *415denied. The judge immediately instructed the jury to “totally disregard the question and not speculate about what the answer might have been.”
We review a decision denying a motion for a mistrial under the abuse of discretion standard. Commonwealth v. Lao, 460 Mass. 12, 19 (2011). “[T]he burden of demonstrating an abuse of discretion is a heavy one.” Commonwealth v. Medeiros, 395 Mass. 336, 351 (1985). The judge was in the best position to assess any potential prejudice and to tailor an appropriate remedy short of declaring a mistrial, where possible. Here, the judge determined that in the circumstances a prompt and forceful instruction to the jury to disregard the question was adequate to protect the defendant’s right to a fair trial. The jury are presumed to follow his instruction to disregard a particular matter. See Commonwealth v. Isabelle, 444 Mass. 416, 420 (2005); Commonwealth v. Qualls, 440 Mass. 576, 584 (2003). The defendant has not shown that the judge abused his discretion.
5. Jury instruction. The defendant contends that because the judge never instructed the jury that they could not return a guilty verdict of felony-murder based on unlawful possession of a firearm, where the jury returned guilty verdicts of felony-murder and unlawful possession of a firearm, and where the jury acquitted the defendant of armed robbery, these circumstances imply that the defendant was impermissibly convicted of felony-murder based on a predicate nonlife felony of unlawful possession of a firearm. We disagree.
The judge instructed the jury that in order to return a guilty verdict of felony-murder, the jury had to be convinced beyond a reasonable doubt that the defendant killed the victim during the commission or attempted commission of an armed robbery. A reasonable jury would understand that their options to find the defendant guilty of felony-murder were limited to a killing committed during the commission of an armed robbery or an attempted armed robbery, and no other felony. Viewing the charge as a whole, no reasonable juror would think he or she could find the defendant guilty of felony-murder committed in the course of the crime of unlawful possession of a firearm. There was no error.
6. Review under G. L. c. 278, § 33E. We have reviewed the *416briefs and the entire record and conclude that there is no reason for us to reduce the degree of guilt or order a new trial.
Judgments affirmed.
he defense in this case was that the defendant had planned a simple drug purchase, but a dispute arose in the course of the transaction and Jiggetts, not the defendant, shot the victim.