Spina, J.
The defendant was convicted of murder in the first degree on theories of deliberate premeditation and felony-murder based on a predicate felony of aggravated rape, as well as aggravated rape. On appeal, the defendant asserts error in the denial of his pretrial motion to dismiss and the denial of his motion for a required finding of not guilty, both based on the sufficiency of the evidence as to the element of consent with respect to aggravated rape. The defendant also challenges the admission of evidence of prior bad acts, and the propriety of the prosecutor’s closing argument. We affirm the convictions and decline to exercise our power under G. L. c. 278, § 33E, to reduce the degree of guilt on the murder conviction or order a new trial.
1. Background. The jury could have found the following facts. We reserve other details for discussion of particular issues.
The victim operated her own beauty salon on Salem Street in Malden. The defendant operated his own video and music shop next door. The defendant sold some of the victim’s merchandise at his store. The victim and the defendant lived together until February 5, 2007, at which time the defendant was ordered to move out of their apartment pursuant to a noncontact abuse prevention order sought by the victim. The order, which specifically allowed the defendant to operate his business, expired February 8, 2008. During 2007, the victim moved to Somerville. Later that year, she moved to Lynn because she thought the defendant was following her. She was planning to move to Florida by the spring of 2008 to get as far away from the defendant as she could.
Some time around July or August, 2007, the victim began dating a man named Yves. In late 2007 or early 2008, the victim told Yves that the defendant wanted to renew their relationship, [399]*399but she had no intention of doing so. The defendant first became aware on Sunday, February 10, 2008, that the victim and Yves were dating. On that day the defendant saw them in front of her salon, which was not open for business on Sundays or Mondays. He confronted them and angrily asked the victim, “Is this the person [you] left me for?” The victim did not answer him. He berated her. She eventually went to her car and drove away. The defendant turned to Yves and said angrily, “People get killed for destroying someone’s relationship.”
On Monday morning, February 11, the defendant unsuccessfully tried five times to reach Edith, one of the victim’s employees, by telephone. When Edith returned the call, the defendant revealed that he had discovered the victim with Yves the day before, that he demanded the victim tell him if she was seeing Yves, and that he followed the victim that afternoon. He further revealed that he was in love with the victim, and that he wanted to live with her. He spoke again with Edith one hour later, and again on February 12.
After the close of business on Tuesday, February 12, the victim met Yves at his home and drove him to her apartment in Lynn. She told Yves that she and the defendant had an argument that day over money from the sale of her hair products at his store. Yves spent the night with her. On Wednesday morning, February 13, she drove Yves to his place of employment in Peabody. He called her cellular telephone at 9:07 a.m. and she said she was still at her apartment. The victim arrived at her beauty salon at about 9:45 a.m. She parked her car in front of the salon and walked inside with her pocketbook and a cup of coffee. At about 11:40 a.m. she told Blandine, an employee, that she was going out and would return. She left without her pocketbook and never returned. The defendant would tell police on February 26 that he had seen her walk past his store on February 13. They spoke, and she told him she was going for coffee. Throughout the day, Blandine made unanswered telephone calls from the salon to the victim’s cellular telephone. She attended to customers by herself.
Within two hours after the victim left the salon the defendant entered and told Blandine he had come for the victim’s pocketbook. He took the pocketbook and left. At about 6 or 6:30 p.m., [400]*400as the defendant was leaving his store for the night, Blandine called to him and asked who would lock the salon, as she did not have a key. He said he would lock the door. As they left, Blandine noticed that the victim’s car was no longer parked in front of the salon. The defendant telephoned Edith that night and told her he tried to reach the victim by calling her cellular telephone, but he received no answer. This was not true — he had not called her cellular telephone number. He asked Edith to return to work, but she refused, saying only the victim could ask her to work.
Shortly after midnight on Thursday, February 14, the defendant’s cousin, with whose family he was staying, returned to her home in Everett after work. The defendant was in his room. At 3:04 a.m. on February 14, the defendant called her cellular telephone and asked if she would lend him a house key so he could go to a pharmacy and get something for his headache. She did not want to give him a key, and told him to contact her when he returned. She locked the door behind him when he went out. At 3:12 a.m. the defendant made a telephone call to a local taxicab company. At 3:25 a.m. a cab from that company picked up the defendant in front of his cousin’s home. The cab driver dropped him off at the corner of Bryant Street and Eastern Avenue in Malden, about four blocks from the victim’s salon, at 3:35 a.m. The defendant’s cousin let him in the house after he telephoned her at 4:19 a.m.
The victim’s cellular telephone records showed which local cellular telephone tower transmitted each call to or from her cellular telephone, that is, the approximate location of her cellular telephone could be ascertained at the beginning and the termination of each call, whether outgoing, answered, or “missed.” As late as 10:58 p.m. on February 13, the victim’s cellular telephone received all calls from the tower at 650 Eastern Avenue in Malden, which served the area where the victim’s salon and the defendant’s store were located. Calls to her cellular telephone after that time and before 9:45 a.m. on February 14 were from the tower at 38 Main Street in Malden, which served the area in Everett where the defendant was living with his cousin’s family.
The victim’s salon did not open for business on February 14. [401]*401Customers went to the defendant’s store to inquire. That afternoon, the defendant placed a sign on the front door of the salon that said “closed for one week.” He told one of the victim’s regular customers and a letter carrier that the salon was closed while the floor was being redone. He told another customer that the victim was “out of State,” and that the salon was getting “new management.” He told a third customer that he did not think the victim would return. The defendant opened the victim’s salon for business on Thursday, February 21, with hairdressers he had hired.
Yves had tried to telephone the victim numerous times beginning at 3:27 p.m. on February 13, but she never answered or returned his calls. The victim’s brother also tried to reach her by telephone on February 14 and 15, but she never answered or returned his calls. The victim’s cellular telephone records for the two-week period beginning with Yves’s call to her at 9:07 a.m. on February 13, showed no outgoing calls. The records indicated unanswered, or “missed,” calls during that period from Yves, the victim’s brother, and Blandine. Both the victim’s and the defendant’s cellular telephone records indicated the defendant had made calls to her cellular telephone in early February, and particularly February 10, the day he confronted her and Yves. He made no calls to her cellular telephone after 10:30 p.m. on February 12, except two calls on February 15 — one at 9:20 a.m., and one at 1:38 p.m.
The victim’s brother drove to her salon after work on February 15, to check on her. He found it closed. A sign read “closed for one week.” He went next door to the defendant’s store and inquired about the victim. The defendant said he did not know where she had gone. The brother asked if the defendant could let him inside the victim’s salon, but the defendant said he did not have a key.1 He said he saw two men changing the lock on the salon door before she left. When the brother asked why she would change the lock, the defendant responded that he and the victim were not really “boy friend and girl friend any more,” and that maybe she did not want him to go to her salon. The brother telephoned the salon the following Friday, February 22, [402]*402and the defendant answered the telephone. He asked if the victim had returned. The defendant said she had not, and that he was there to clean. When asked how he was able to get into the salon, he said he obtained a key from the landlord. The brother went to the salon on Saturday, February 23. It was closed, but the sign was gone. He went to the defendant’s store and asked him for the landlord’s telephone number so he could get a key to enter the salon. The defendant told him he did not have the landlord’s telephone number. The brother then drove to the Lynn police department for assistance.
On Wednesday, February 27, two officers of the Malden police department were returning from an interview with Blandine when they discovered the victim’s car parked on Faulkner Street, approximately two blocks from the salon, and two blocks from the intersection of Bryant Street and Eastern Avenue, where the cab driver dropped off the defendant in the early morning hours of February 14. The car was towed to the Malden police station, where it was searched. The victim’s pocketbook was on the floor in front of the passenger seat. The contents of the pocketbook were inventoried, and included a duplicate key to the victim’s car (the original was found above a ceiling panel in the defendant’s store), her cellular telephone, and her copy of the abuse prevention order dated February 5, 2007 (with the modification allowing the defendant to operate his business).
The victim’s body was found in the trunk of the car. An autopsy revealed that the cause of death was asphyxia caused by smothering and compression of the victim’s airway, and that death would have followed shortly after oxygen deprivation for a period of from four to six minutes. Internal bruising and bleeding in her neck muscles, as well as evidence of petechia (seepage of blood from raptured small blood vessels into surrounding tissue), were consistent with asphyxia. Abrasions and evidence of bleeding of the inside of the victim’s lips indicated forceful contact against her teeth. Abrasions to her lips, nose, left cheek, and chin were consistent with blunt trauma injury. She also had contusions in the outside of her right upper arm and her left elbow.
Deoxyribonucleic acid (DNA) evidence from sperm cells collected at the autopsy indicated that the defendant was the source of DNA in a vaginal swab, based on a statistical likelihood of a [403]*403random match being one in 60.9 quintillion in the African-American population2; and he was the source of DNA in an anal swab, based on a statistical likelihood of a random match being one in 21.6 quadrillion in the African-American population. Yves was excluded as a source.
DNA recovered from scrapings under fingernails from both hands of the victim was examined at the Y chromosome. The defendant and his paternal relatives were determined to have DNA consistent with this profile, but this specific profile was not observed in the database for African-American males at the Y chromosome. The likelihood of a random match was one in 793. This was characterized as the “best statistic” available for this database. Yves was excluded as to samples from the victim’s left hand, but inconclusive as to samples from her right hand.
DNA from a piece of chewing gum affixed to the collar of the victim’s shirt was determined to match that of the defendant, with a statistical likelihood of a random match being one in 60.9 quintillion.
The defendant testified that he and the victim had an ongoing relationship, including sexual relations, notwithstanding the abuse prevention order. He also testified that he and the victim had consensual sexual intercourse in his store on Tuesday, February 12, 2008.
2. Motion to dismiss. The defendant asserts error in the denial of his motion to dismiss the indictment alleging aggravated rape because there was insufficient evidence presented to the grand jury to show probable cause that the sexual intercourse between him and the victim was not consensual. Because he was convicted of both deliberately premeditated murder and felony-murder (based on the predicate felony aggravated rape), the separate conviction of aggravated rape was not duplicative. See Commonwealth v. Caldwell, 459 Mass. 271, 288 n.21 (2011), and cases cited. He is entitled to our consideration of the issue.
“[A]t the very least the grand jury must hear sufficient evidence to establish the identity of the accused . . . and probable cause to arrest him” (citations omitted). Commonwealth v. McCarthy, 385 Mass. 160, 163 (1982). Probable cause to arrest is [404]*404“reasonably trustworthy information . . . sufficient to warrant a prudent man in believing that the defendant had committed or was committing an offense.” Commonwealth v. Stevens, 362 Mass. 24, 26 (1972), quoting Beck v. Ohio, 379 U.S. 89, 91 (1964). The McCarthy case represents an exception to the rule that courts ordinarily do not inquire into the competency or sufficiency of the evidence presented to the grand jury. Commonwealth v. Moran, 453 Mass. 880, 883-884 (2009). Our case law recognizes that fundamental fairness requires that an indictment be dismissed where the “grand jury receive[s] no evidence of criminality on the part of the accused” (emphasis added). Id. at 884, quoting Commonwealth v. Coonan, 428 Mass. 823, 825 (1999). This is not such a case.
The grand jury heard evidence that the defendant was the victim’s former boy friend, that she had obtained an abuse prevention order against him that recently expired, and that she had a new boy friend. The grand jury also heard that the defendant and the victim argued the Sunday before she disappeared and again the day before she disappeared. They heard evidence that the victim left her salon on the morning of February 13, 2008, and never returned. That afternoon, the defendant entered her salon and asked for the victim’s pocketbook, saying he was going to bring it to her. The defendant told police he last saw the victim on the morning of February 13 when she walked by him as he stood in the doorway of his store, and that he had no idea where she had gone. He never told police he had retrieved her pocketbook to give to her, as he told the victim’s employee he was going to do. The grand jury were presented evidence that the victim’s pocketbook was found in the front seat of her car, her body was found in the trunk, and the defendant’s DNA was found in the victim’s vagina and anus. The victim had been strangled to death. Her face and neck were bruised, and she had blood in her mouth.
There was sufficient evidence presented to the grand jury to establish probable cause to believe the defendant had had sexual and unnatural sexual intercourse with the victim, that he compelled her to submit by force and against her will, and that serious bodily injury resulted. The judge did not err in denying the defendant’s motion to dismiss the aggravated rape indictment, [405]*405as there was sufficient evidence from which the grand jury could have inferred the victim did not consent to intercourse with the defendant.
The defendant further argues that the felony-murder conviction must be dismissed because it was based on the predicate felony of aggravated rape, and the grand jury were not presented with sufficient evidence of lack of consent. He did not file a pretrial motion to dismiss so much of the murder indictment as advances the theory of felony-murder, nor did he make this argument in the trial court. The aggravated rape indictment and the murder indictment were returned by different grand juries. The defendant has not furnished the grand jury minutes concerning the murder indictment, and he has not challenged the sufficiency of the evidence presented to the grand jury that returned the indictment charging murder.
We review claims of unpreserved error in capital cases under the standard of a substantial likelihood of a miscarriage of justice. See Commonwealth v. Wright, 411 Mass. 678, 682 (1992). Here, we have no way of knowing what evidence was presented to the grand jury that returned the murder indictment. However, that does not matter. The defendant does not contend that the grand jury could not have handed down the murder indictment. A valid indictment for murder in the first degree that uses the language of the indictment form provided in G. L. c. 277, § 79, as here, charges murder by whatever means it may have been committed, regardless of the theory of murder presented to the grand jury. See Commonwealth v. DePace, 442 Mass. 739, 742-744 (2004), cert. denied, 544 U.S. 980 (2005); Commonwealth v. Daughtry, 417 Mass. 136, 141-143 (1994). Because he could not have prevailed on a motion to dismiss based on the argument he now advances, there could be no error and no substantial likelihood of a miscarriage of justice.
3. Motion for required finding. The defendant contends that it was error to deny his motion for a required finding of not guilty as to the indictment alleging aggravated rape and so much of the murder indictment that relied on a theory of felony-murder based on the predicate felony of aggravated rape, because the Commonwealth failed to prove beyond a reasonable doubt that the victim did not consent to sexual intercourse with the defendant. [406]*406We review the evidence at the close of the Commonwealth’s case in its light most favorable to the Commonwealth. See Commonwealth v. Latimore, 378 Mass. 671, 676-677 (1979).
The defendant berated the victim for leaving him for Yves, and he suggested to Yves that he could be killed for breaking up their relationship. The defendant telephoned Edith on February 11, upset at having found the victim and Yves together the day before. He admitted following the victim, and confessed his love for her and a desire to be with her. The victim simply had no further interest in him, and the defendant admitted as much to the victim’s brother in response to the brother’s question about why she would change the lock to her salon. The jury could have inferred from the injuries to the victim’s head and neck; evidence of the defendant’s chewing gum being stuck to the collar of her shirt; and the fact that she was never seen again after she left her salon on the morning of February 13, after saying she would be right back, that the defendant, angry and jealous that the victim was having a relationship with Yves, something he had discovered recently, had beaten the victim into submitting to sexual intercourse to which she did not consent. The evidence of lack of consent, though circumstantial, was very powerful, and supports a finding beyond a reasonable doubt that the victim did not consent to sexual intercourse or unnatural sexual intercourse with the defendant.
4. Prior bad acts. The defendant argues that certain evidence of prior bad acts erroneously was admitted, as follows.
a. Victim’s affidavit. The victim’s affidavit in support of her application for an abuse prevention order dated February 5, 2007, and the order itself, were admitted over objection. The affidavit states, “I want this restraining order because [the defendant] is violent. He makes me scared. I want him to stay away from me so that he won’t hurt me again.” The judge gave a limiting instruction to the jury just before they heard the testimony about the victim’s affidavit and the abuse prevention order, and again just before those documents were admitted in evidence. She instructed the jury that the evidence in question, if they accepted it, could be considered only as to the victim’s state of mind, whether she would have consented to sexual intercourse with the defendant, the nature of the relationship between [407]*407the victim and the defendant, and the defendant’s motive as to any events about which they would hear. The defendant contends this was inadmissible hearsay that violated his constitutional right of confrontation, and that it was so remote (the order issued approximately one year before the victim’s death) that its potential for prejudice outweighed its probative value.
b. Victim’s statements to her brother. The victim’s brother testified, over objection, to a conversation he had with the victim on February 4, 2007, approximately one year before her death. The victim related to her brother that she and the defendant had an argument, that the defendant then wanted to have sex with her, but she refused. The defendant then pushed her down, put one hand on her throat, and threatened to kill her with a knife he held in his other hand. He told her, “You see how easy it is for me to kill you?” She related how she cried, then telephoned her mother. The victim’s brother testified that he urged her to go to court and get a protective order, which she did the next day. The judge gave the jury a contemporaneous limiting instruction substantially similar to the one she gave as to the affidavit and abuse prevention order. The defendant argues that this was inadmissible hearsay that violated his constitutional right to confrontation, and that because it was so remote, its potential for prejudice outweighed its probative value.
The victim’s brother also testified, over objection, that in late 2007 or early 2008, the victim said she wanted to move to Florida to get as far away as possible from the defendant. She was upset because she thought the defendant had been following her, and he never gave her the proceeds of sales of her merchandise that he conducted from his store. She also was upset about the video camera inside her salon that he used to monitor her activities from his store. The judge contemporaneously instructed the jury that the same limiting instructions previously given applied to this testimony. These three limiting instructions were given very close in time to one another, over a space of ten transcript pages. The defendant asserts this was inadmissible hearsay that violated his right to confrontation. He further argues that its potential for prejudice outweighed its probative value where the statements were ambiguous: the victim continued to meet with him and conduct her business with him from February, 2007, to February, 2008.
[408]*408c. Victim’s statements to Yves. Yves testified, over objection, that sometime toward the end of 2007 or in early 2008, the victim told him that she and the defendant had an argument over his desire to renew their relationship and her refusal to do so. She expressed concern over his violent tendencies and his possessiveness. Yves also testified, without objection, to a conversation he had with the victim on Tuesday evening, February 12, 2008, in which she said she and the defendant had an argument that day about his encounter with her and Yves the previous Sunday. The victim and the defendant also argued about the money she claimed he owed her from the sale of her merchandise in his store. The judge instructed the jury they could consider this evidence, if they accepted it, only on the question of the victim’s state of mind, and specifically, whether she would have consented to sexual intercourse with the defendant. The defendant argues that this was inadmissible hearsay that violated his constitutional right to confrontation, and its potential for prejudice outweighed its probative value where the statements were ambiguous in view of the victim’s continued business contact with the defendant over the last year of her life.
Evidence of a defendant’s prior bad acts are not admissible to show bad character or propensity to commit the crime for which he has been charged. It may, however, be admitted, if relevant, for some other purpose, such as proving common scheme, pattern of operation, preparation, opportunity, nature of relationship, knowledge, intent, motive, identity, or absence of accident or mistake. See Commonwealth v. Helfant, 398 Mass. 214, 224-225 (1986); Mass. G. Evid. § 404(b) (2011). Relevant evidence is generally admissible, but it “may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice.” Mass. G. Evid., supra at § 403 at 35. See Commonwealth v. Helfant, supra at 225; Mass. G. Evid., supra at § 402.
Absence of consent is an essential element of the crime of rape, whether aggravated or unaggravated. See Commonwealth v. Sherry, 386 Mass. 682, 687-688 (1982); Commonwealth v. McCan, 277 Mass. 199, 203 (1931). The victim’s state of mind at the time of the sexual intercourse is relevant on the issue of consent.3 Commonwealth v. Gardner, 350 Mass. 664, 668 (1966); [409]*409Commonwealth v. Dies, 248 Mass. 482, 489 (1924). All the evidence in question was relevant to the victim’s state of mind, specifically whether she would have consented to sexual intercourse with the defendant. Although the victim’s affidavit and the protective order were more than one year old, and the protective order had expired, there was evidence spanning the entire last year of the victim’s life from which the jury could infer a state of mind in the victim that was inconsistent with consent and consistent with an absence of consent. Moreover, there was evidence that the victim kept a copy of the abuse prevention order in her pocket book at the time of her death. A jury could reasonably infer that she was resolved over the last year of her life to keep as much distance from the defendant as possible.
There is no merit to the defendant’s claim that certain evidence of the victim’s state of mind was inadmissible because it was ambiguous. There is no inherent ambiguity in any of the victim’s statements about which the defendant complains. What the defendant refers to as an ambiguity is merely a potential conflict with other evidence, e.g., her ongoing business relations with the defendant. Cf. Commonwealth v. Lewin (No. 2), 407 Mass. 629, 631 (1990), and cases cited (statement to court personnel by defendant charged with murder in connection with possibility of plea bargain to effect that he would plead guilty to manslaughter had ambiguous probative value outweighed by prejudicial effect). Such conflicts in evidence, if any, are for the jury to resolve and do not render evidence inadmissible.
The evidence admitted with the limitation that it could be considered as to the victim’s state of mind and whether she would have consented to sexual intercourse with the defendant was not inadmissible hearsay because it was not admitted for the truth of the matter asserted by the victim. Rather it was admitted solely as evidence of her state of mind, without regard to whether it was true. See Commonwealth v. Montanez, 439 Mass. 441,447 (2003). [410]*410See also Mass. G. Evid., supra at § 801(c) at 233. As such, the evidence was neither evidence of prior bad acts, nor was it “testimonial” for purposes of the constitutional right to confrontation. See Commonwealth v. Hurley, 455 Mass. 53, 65 n.12 (2009). There was no error in admitting any of the evidence in question for the limited purpose of showing the victim’s state of mind on the issue of consent to have intercourse with the defendant.
The question as to the propriety of the limiting instruction that permitted use of the questioned evidence in determining the nature of the relationship of the parties and the defendant’s motives is more complex. This evidence consisted of the abuse prevention order and supporting affidavit, and the testimony of the victim’s brother as to his conversations with the victim. It did not include Yves’s testimony as to his conversations with the victim, as that testimony was admitted solely on the question of the victim’s state of mind and the question of consent.
The abuse prevention order properly was admitted as evidence both of the nature of the relationship between the victim and the defendant, and as to his motive to kill her. The victim kept the abuse prevention order with her even after it expired, until her death. It defined the permissible limits of their ongoing relationship. That is, it permitted the defendant to operate his business next door to hers, but otherwise it ordered him to have no contact with her. More significantly, the victim also had in her pocketbook a summons to appear and testify against the defendant in a criminal matter scheduled for trial on February 26, 2008, based in part on an alleged violation of the abuse prevention order. The defendant had been aware both of the abuse prevention order and the pending criminal case scheduled for trial on February 26. These documents had ongoing vitality and were properly admitted, as limited. See Commonwealth v. Sharpe, 454 Mass. 135, 144-145 (2009), and cases cited.
The victim’s affidavit in support of the abuse prevention order should not have been admitted as evidence of the defendant’s motive to kill the victim or as evidence of the nature of the relationship of the parties. As such, it was offered to prove the truth of the matters asserted therein, and was hearsay that did not fall within any exception to the hearsay rule. Moreover, the affidavit was testimonial per se in the constitutional sense, and its [411]*411admission to prove motive or the nature of the relationship of the parties violated the defendant’s right to confrontation. See Commonwealth v. Simon, 456 Mass. 280, 297, cert. denied, 131 S. Ct. 181 (2010). The constitutional issue was properly preserved, so we review the erroneous admission of the victim’s affidavit for the purpose of showing motive to kill and the nature of the relationship to determine whether it was harmless beyond a reasonable doubt. See Commonwealth v. Vinnie, 428 Mass. 161, 163, cert. denied, 525 U.S. 1007 (1998). However, we are satisfied that the evidence did not contribute to the verdict. See Commonwealth v. Molina, 439 Mass. 206, 212 (2003). The affidavit was extremely brief and contained nothing that stood out among the voluminous segments of admissible and overwhelming evidence of guilt, especially where the abuse prevention order was properly admitted.
The testimony of the victim’s brother as to his conversations with the victim should not have been admitted for the purpose of showing the nature of the relationship of the parties, or the defendant’s motive to kill the victim. The evidence necessarily had to have been admitted for the truth of the matters related by the victim to her brother. As such, her statements to her brother were hearsay and did not fall within any recognized exception to the hearsay rule. They were not testimonial statements in the constitutional sense because they were not made in response to police questioning, they had not been formalized in any respect, and they were not made in circumstances that would have suggested to a reasonable person in the victim’s position that the statements would be used against the defendant in a criminal investigation or prosecution. Commonwealth v. Gonsalves, 445 Mass. 1, 12-13 (2005), cert. denied, 548 U.S. 926 (2006).
Because the hearsay issue was preserved, we review for prejudicial error. See Commonwealth v. Flebotte, 417 Mass. 348, 353 (1994). We are satisfied that the erroneous admission of the victim’s statements to prove motive or the nature of the relationship of the parties “did not influence the jury, or had but very slight effect.” Id., quoting Commonwealth v. Peruzzi, 15 Mass. App. Ct. 437, 445 (1983). There was abundant admissible evidence that the relationship between the victim and the defendant was poor, and abundant admissible evidence that the defendant had a motive to kill the victim. The abuse prevention order [412]*412and the summons were properly admitted for this purpose. See Commonwealth v. Sharpe, supra; Commonwealth v. Gil, 393 Mass. 204, 215-216 (1984). Yves’s testimony about his observations of the defendant’s hostile encounter with himself and the victim on Sunday, February 10, 2008, and the manner in which the defendant berated the victim and implied that he could kill Yves, presented graphic evidence of motive. The case against the defendant was overwhelming. We conclude that the defendant has shown no prejudice.
5. Prosecutor’s closing argument. The defendant cites three instances where he claims the prosecutor made improper argument in her closing. He claims she “misstated the length of time of strangulation.” There was no objection, so we review to determine if any error created a substantial likelihood of a miscarriage of justice. See Commonwealth v. Wright, 411 Mass. 678, 682 (1992). The prosecutor argued that strangulation from between four to six minutes caused death from oxygen deprivation to the brain, and also caused hemorrhaging in the neck. The Commonwealth’s pathologist testified that “[bjrain damage, once you exclude oxygen, once the body no longer has an oxygen supply, will occur in four to six minutes. And death will occur shortly thereafter.” The pathologist was uncertain about how long pressure would have to be applied to the neck to cause the hemorrhaging observed in the victim’s neck. While the prosecutor’s argument that strangulation that cut off oxygen to the victim’s brain lasted from four to six minutes was based on an inference fairly drawn from the evidence, see Commonwealth v. Morganti, 455 Mass. 388, 407 (2009), the same cannot be said of the amount of time of strangulation needed to cause the hemorrhaging. Nonetheless, we fail to see how this language, which does not appear to have been an intentional misstatement, created a substantial likelihood of a miscarriage of justice.
The defendant next argues that the prosecutor mischaracterized DNA evidence, in particular, DNA taken from fingernail scrapings of the victim. We have reviewed the transcript and conclude that the prosecutor did not mischaracterize this particular portion of the evidence. This was some of the weakest DNA evidence, and the specific profile seen was not observed in the database for African-American males at the Y chromosome. The [413]*413likelihood of a random match was only one in 793, but the expert witness characterized this as the “best statistic” available for this database. This particular portion of the trial testimony was difficult and awkward. The expert’s “best statistic” comment was meant to be something of an apology. The prosecutor’s argument fairly tracked the testimony, and her use of the expert witness’s term “best statistic” available conveyed the same apologetic tone. The prosecutor did not misuse the term “best statistic” available to overstate the value of the testimony. The evidence of the defendant’s DNA on the chewing gum stuck to the victim’s shirt was far more damaging, and implied he was having sexual relations with her at the time she was murdered. There was no error.
Finally, the defendant argues that the prosecutor misused propensity evidence by arguing that the defendant acted “similarly” in the past. The prosecutor recalled that the victim obtained the protective order because the defendant put his hand over her mouth and “threatened to kill her” on February 4, 2007. The prosecutor also argued that the victim put up with the defendant coming in and out of her salon and talking about renewing their relationship because “she knew the violence that he was capable of inflicting.” The evidence to which the prosecutor was referring had been admitted for a limited purpose. Trial counsel objected and moved for a mistrial. The judge denied the motion for a mistrial. The judge stated that she was watching the prosecutor during this portion of her closing argument and the prosecutor appeared to have realized she might have crossed the line, and stopped. The judge noted that the prosecutor’s argument at that point “just sort of died and went nowhere.” The judge gave a very forceful curative instruction chastising the prosecutor, saying:
“Ladies and gentlemen, there was something said by [the prosecutor] in her closing argument that I need to address with you because it was really improper and not right or legal. And it relates to the instruction that I’ve been giving you all along, my limiting instruction, and how you can consider certain evidence.
“I again tell you, and you know I have said this repeat[414]*414edly, but I must say it again, and I will say it again tomorrow, the restraining order and all of that evidence that surrounded that, you cannot consider that as evidence that [the defendant] committed these crimes. You cannot consider any evidence of any similarities or dissimilarities. It has nothing to do with that. What you may consider it for, as I’ve told you repeatedly, is for motive, whether [the victim] would have consented to sexual contact with [the defendant], what her state of mind was, and what their relationship was. But you may not consider anything surrounding the restraining order.”
The judge continued, giving the same limiting instruction as to the summons for the February 26, 2008, criminal trial. The jury are presumed to have followed this instruction. See Commonwealth v. Jenkins, 458 Mass. 791, 802 (2011); Commonwealth v. Auclair, 444 Mass. 348, 360 (2005). We are confident the prosecutor’s statements did not make a difference in the jury’s verdict, given the judge’s prompt and forceful instruction.
6. Review under G. L. c. 278, § 33E. We have reviewed the entire record, the briefs, and the arguments, and see no reason to reduce the degree of guilty on the murder conviction or order a new trial.
Judgments affirmed.