The defendant, Robert Kosilek, was convicted of murder in the first degree under theories of premeditated and deliberate murder and extreme atrocity or cruelty for the death of his wife, Cheiyl Kosilek. On appeal, the defendant contends that his conviction must be reversed principally because of: (1) errors in jury instructions; (2) limitation of cross-examination on the issue of self-defense; and (3) improper statements in the prosecutor’s closing argument. The defendant also challenges the judge’s denial of his motion for a required finding of not guilty, and alleges ineffective assistance of trial counsel.2 We have considered these arguments and have reviewed the entire record pursuant to G. L. c. 278, § 33E (1994 ed.). We affirm the conviction.
1. Facts. We review the facts in the light most favorable to the Commonwealth. Commonwealth v. Morgan, 422 Mass. 373, 374 (1996). The victim’s body was discovered in the back seat of her automobile in a shopping mall parking lot in North Attleborough on the evening of Sunday, May 20, 1990, after the mall had closed for the evening. She had been strangled with a rope and a wire.
A taxicab driver testified , that he picked up the defendant from the same mall on the afternoon of May 20 and drove him to a store located about one-half mile from the defendant’s house in Mansfield. That evening, police in North Attleborough received a telephone call from the defendant *451stating that his wife had not come home that evening and asking whether there had been any report of an automobile accident in which she might have been involved. The police told the defendant that they had located his wife’s automobile, and they asked him to come to the police station, which he agreed to do. At the defendant’s request, an officer was sent to pick him up and bring him to the station.3 At the station, Lieutenant Michael Gould informed the defendant that “a body was found in the back seat” of his wife’s automobile. Gould questioned the defendant about his actions and the victim’s actions during the day. The defendant stated that the victim had gone to work for part of the day and intended to stop at the mall on the way home; he also said that he had spent the day working around the house.4
The following day, May 21, 1990, the defendant was again asked to come to the police station to speak with Gould. During the interview, Gould advised the defendant that he was a suspect and informed him of his Miranda rights. Gould told the defendant that the police had spoken with the victim’s son, Timothy McCaul, who had lived with the defendant and the victim. McCaul told the police that he had been working during the day of the murder, that he called home at about 5 p.m. to ask for a ride home, and that no one answered the telephone. The defendant noted that Timothy often dialed wrong numbers, and he suggested that he may have been in the shower at the time of the call and failed to hear it. During this second interview with police, the defendant excused himself to go downstairs for cigarettes. Once downstairs, the defendant called up to the officers that he was going to get a lawyer, and left.5
On May 22, 1990, shortly after midnight, the defendant was involved in an automobile accident in Bedford. When a police officer arrived at the scene, he observed the defendant, dressed in women’s clothing, seated in his vehicle, which had crashed into a stop sign and some shrubs. The officer administered field sobriety tests, determined that the defen*452dont was not intoxicated, and called a taxi to drive the defendant home.
Two days later, on the afternoon of May 24, 1990, police in New Rochelle, New York, stopped the defendant for speeding. After the officer observed a bottle of vodka, two-thirds full, and two cans of beer in the automobile, and smelled alcohol on the defendant’s breath, he arrested the defendant for driving while intoxicated and brought him to the police station. At some point, the defendant remarked to the arresting officer, “You would be drunk too if the police thought you killed your wife.” Later, at the New Rochelle police station, the defendant stated, “Look, I had a fifteen year old son and a wife. I can’t call my wife. I murdered my wife. Now, I need to call a psychiatrist now.” The defendant was taken to the psychiatric unit of a New York hospital and subsequently was brought back to Massachusetts by the Massachusetts State police.
About two and one-half years later, in October of 1992, the defendant gave a series of recorded interviews to a television news reporter. An audiotape recording of one of the interview sessions was played for the jury. During the interview, the defendant stated that: on the day of the murder, he and the victim had been in an argument; the victim threw boiling tea into the defendant’s face; he then knocked the victim down; she grabbed a butcher knife and chased the defendant into another room, threatening to kill him; he picked up a piece of wire that had been on a table; and this was all he was able to recall until he woke up days later in the hospital. The defendant stated in the interview that he “probably, because of the trauma of it . . . went into a black out at that moment.” He also said, “Apparently, I did take her life. It was probably in self-defense.”
2. Jury instructions. The defendant points to a number of mistakes, omissions, or misstatements in the jury charge which, he contends, created a substantial likelihood of a miscarriage of justice, either in whole or in part.
a. Deliberate premeditation. The instructions for deliberate and premeditated murder (the full text of which is set out in the margin6) contained two mistakes. First, in the course of *453explaining the concept of deliberation, the judge included the following statement:
“Deliberation may be a matter of days, hours, or indeed, seconds. First the deliberation and premeditation, then the decision to kill, and lastly, the killing in furtherance of that decision. All of this may occur within a few seconds. However, it does not exclude action that is taken so quickly that there is no time to think about the action and then determine to do if (emphasis added).
The emphasized portion of the statement is incorrect as a matter of law. The Commonwealth does not argue otherwise. Cf. Commonwealth v. Callahan, 401 Mass. 627, 633 (1988) (deliberate premeditation “excludes action which is taken so *454spontaneously that there is no time to think”). There was no objection to the instruction.7
When the erroneous statement is read in the context of the entire instruction, it is clear that the mistake was not prejudicial. The error is sandwiched between accurate statements of the law regarding premeditation and deliberation. In particular, the judge followed the error with a sentence stating in part that “the Commonwealth must show that the defendant’s resolve to kill was the product of cool reflection.” This statement, and others like it, substantially corrected any misconception which may have arisen in the minds of the jurors. Indeed, if the transcript is correct, the error was not even noticed by counsel. Taken as a whole, then, the instruction did not create a substantial likelihood of a miscarriage of justice. See Commonwealth v. Campbell, 378 Mass. 680, 706 (1979); Commonwealth v. Diaz, 19 Mass. App. Ct. 29, 38-39 (1984).
The second mistake in the premeditation instruction occurred in the course of the judge’s discussion of the effect of any mental impairment on the defendant’s ability deliberately to premeditate. The judge stated, in part:
“You should weigh the defendant’s mental impairment, if any, in evaluating any evidence that he formed a plan to kill the victim after deliberation and reflection. The Commonwealth does not have to prove that the defendant was entirely free of mental impairment, but the Commonwealth does have to prove that the defendant was so impaired that he lost the ability to deliberately premeditate” (emphasis added).
Once again, the emphasized portion of the statement is incorrect as a matter of law. See Commonwealth v. Meinholz, 420 Mass. 633, 637-638 (1995). At trial, both the Commonwealth and defense counsel brought this to the judge’s at*455tention, and the judge provided a supplementary instruction in an attempt to cure the error.8 The additional instruction — to which the defendant did not object — did not refer specifically to impairment or intoxication.
The Commonwealth contends that any error was cured by the instructions taken as a whole, which set out several times the jury’s requirement to consider the effect of any mental impairment. We agree. “[Wjhere there is evidence of the effects of the consumption of drugs [or alcohol] that, if believed, would be relevant to a defendant’s state of mind or knowledge, then a simple instruction is required.” Commonwealth v. Morgan, 422 Mass. 373, 377 (1996), citing Commonwealth v. Sires, 413 Mass. 292, 300-301 (1992). Here, the instructions on mental impairment as a whole satisfied these requirements. As with the earlier error, the misstatement is preceded and followed by accurate statements of the controlling law on the issue of mental impairment. Furthermore, the judge’s supplementary instruction on the Commonwealth’s burden served to dissipate any lingering confusion resulting from the misstatement. We perceive no prejudice to the defendant that would result in a miscarriage of justice. See Commonwealth v. Giguere, 420 Mass. 226, 232 (1995).9
b. Extreme atrocity or cruelty. The judge gave the instruc*456tian on extreme atrocity or cruelty that we disapproved in Commonwealth v. Hunter, 416 Mass. 831 (1994).10 The defendant did not object. We review the instruction only to see whether it caused a substantial likelihood of a miscarriage of justice. See Commonwealth v. Semedo, 422 Mass. 716, 726 (1996). Where, as here, the jury found the defendant guilty on the theory of premeditated and deliberate murder, as well as extreme atrocity or cruelty, it is highly unlikely that the defendant was prejudiced by the instruction. See Commonwealth v. Blackwell, 422 Mass. 294, 300 (1996) (Hunter error not prejudicial where jury clearly found defendant guilty on another theory of murder).
c. Voluntariness-humane practice. Several inculpatory statements made by the defendant were admitted in evidence. Motions to suppress the statements were denied. The defendant does not appeal from the denial of these motions, but instead argues that the instruction on the voluntariness of these statements was error because it failed to enumerate the factors to be considered in making this determination, especially the effect of intoxication.11 The defendant did not object to this aspect of the instruction. We conclude that the instruction was sufficient in light of the evidence at trial. “Although the *457instruction appropriately might have contained more detail, it was correct.” Commonwealth v. Grenier, 415 Mass. 680, 688 (1993) . See Commonwealth v. Mello, 420 Mass. 375, 385 (1995). We discern no substantial likelihood of a miscarriage of justice arising from the charge on voluntariness.
d. Prior inconsistent statements. During his instructions on the evidentiary weight of prior inconsistent statements, the judge concluded an otherwise accurate description of the law by saying, “The present statement is relevant only to the witness’s credibility, and you may not take it as proof of any fact contained in it” (emphasis added). The instruction would be accurate if the word “prior” is substituted for the word “present.” See Commonwealth v. Pierce, 419 Mass. 28, 39-41 (1994) . See generally P.J. Liacos, Massachusetts Evidence § 6.6.2 (c), at 282-286 (6th ed. 1994). Even as the record indicates, the mistake is relatively innocuous and there was no objection.
Furthermore, the Commonwealth notes that there was no evidence of any prior statements that were inconsistent with testimony at trial. The defendant offers no examples of actual or potential prejudice as a result of the misstatement. We conclude that any error in the instruction did not create a substantial likelihood of a miscarriage of justice. See Commonwealth v. Anderson, 396 Mass. 306, 316 (1985).
e. Cumulative error and ineffective assistance of counsel. The defendant argues that, even if none of the above errors requires reversal separately, the combined effect of the mistakes was so prejudicial that it created a substantial likelihood of a miscarriage of justice. We disagree. The cumulative error was no more prejudicial than the individual errors, which had minimal impact. See Commonwealth v. Fuller, 421 Mass. 400, 410-413 (1995); Commonwealth v. Garcia, 379 Mass. 422, 441-442 (1980).
In the alternative, the defendant asks us to determine that the trial counsel’s failure to object to these errors constituted ineffective assistance of counsel. “[I]f an error not objected to by trial counsel does not create a substantial likelihood of a miscarriage of justice, see G. L. c. 278, § 33E ... a claim of ineffective assistance of counsel with respect to such error will not succeed, Commonwealth v. Wright, 411 Mass. 678, *458681-682 (1992).” Commonwealth, v. Waite, 422 Mass. 792, 807 (1996).
3. Evidentiary error. The defendant claimed that he had been acting in self-defense. He told a television news reporter (in an audiotaped interview that was played for the jury) that, on the day of his wife’s death, she had attacked him with a pan of boiling tea and a large kitchen knife.12 There was evidence that the defendant had bums on his hands that were consistent with the story. In an attempt to develop this theory, defense counsel sought to cross-examine the victim’s son about any arguments he may have had with his mother, apparently to elicit testimony that she had reacted violently in some instances. The Commonwealth objected. At sidebar, defense counsel made an offer of proof. The judge sustained the objection, noting that the fact that a mother may have hit her son while disciplining him was not relevant to the self-defense issue. The relevant portion of the colloquy is set out in the margin.13
The judge has broad discretion to determine the extent of cross-examination, see Commonwealth v. Clarke, 418 Mass. *459207, 212 (1994), and to exclude evidence of limited probative value, see Commonwealth v. Palmariello, 392 Mass. 126, 137-138 (1984). Evidence of past violent acts against a third party by the victim is admissible where there is evidence of “recent, specific instances of the victim’s violent conduct, known to the defendant at the time of the homicide.” Commonwealth v. Fontes, 396 Mass. 733, 735 (1986). Determining which types of specific acts by the victim are relevant to the issue of self-defense is a matter “left to the sound discretion of the judge.” Commonwealth v. Rodriquez, 418 Mass. 1, 6 (1994). Here, even if the defendant knew that the victim had used physical force to discipline her son on specific recent occasions (an assertion not at all clear from the record), the judge had discretion to exclude the evidence on the basis of its limited probative value. There was no error. Cf. Commonwealth v. Rodriquez, supra.
4. Prosecutorial error. In his closing statement, the prosecutor referred to the defendant on several occasions as a “liar” who had constructed a “cunning charade” to mislead the police. There was no objection. The defendant argues that the prosecutor improperly gave his personal opinion of the defendant’s guilt and credibility. See Commonwealth v. Chavis, 415 Mass. 703, 713 (1993); S.J.C. Rule 3:07, Canon 7, DR 7-106 (C) (4), as appearing in 382 Mass. 787 (1981). But cf. Commonwealth v. Yesilciman, 406 Mass. 736, 745-746 (1990).
It is well established that “[a] prosecutor may not assert his or her personal opinion as to the credibility of a witness or the guilt of an accused.” Commonwealth v. Chavis, supra at 713. “However, the prosecutor may comment on evidence developed at trial and draw inferences from such evidence.” Id. In this case the prosecutor probably crossed the line of fair comment on the evidence and offered his opinion of the defendant’s credibility. We conclude, however, that, in the context of the judge’s instructions14 and the weight of the Commonwealth’s case, any error was not so prejudicial as to create a substantial likelihood of a miscarriage of justice. See Commonwealth v. Campbell, 394 Mass. 77, 88 & n.ll (1985); Commonwealth v. Cameron, 385 Mass. 660, 669-670 (1982); *460Commonwealth v. MacDonald, 368 Mass. 395, 400-401 (1975).
5. Sufficiency of evidence. The defendant argues that there was insufficient evidence for a guilty finding on either the premeditated and deliberate murder theory or the extreme atrocity theory, and therefore, the judge erred in denying his motion for a required finding of not guilty. We disagree. There was ample evidence to convict on both theories. With regard to deliberate premeditation, the evidence would permit a rational jury to infer that the defendant waited until the victim’s son was at work, that he approached his wife from behind with a wire, and strangled her by tightening the wire around her neck. With regard to extreme atrocity or cruelty, the prosecution’s expert testified that: there were multiple wounds on the victim’s body; she was strangled by a wire and then a rope; she was conscious for at least fifteen seconds after strangulation began and remained alive for three to five minutes; and there were indications of a conscious struggle. These facts amply support a finding of premeditated and deliberate murder, see Commonwealth v. Judge, 420 Mass. 433, 441 (1995); Commonwealth v. Chipman, 418 Mass. 262, 269-270 (1994); Commonwealth v. Basch, 386 Mass. 620, 622 (1982), as well as murder by extreme atrocity or cruelty, see Commonwealth v. Simmons, 419 Mass. 426 (1995); Commonwealth v. Tanner, 417 Mass. 1, 2 (1994).
6. Relief under G. L. c. 278, § 33E. We have reviewed the entire record pursuant to our responsibilities under G. L. c. 278, § 33E. There was sufficient evidence to convict, and any errors did not create a substantial likelihood of a miscarriage of justice. Therefore, we decline to exercise our extraordinary power to reverse the conviction or reduce the degree of guilt.
Judgment affirmed.
The defendant is represented by different counsel on appeal.
The officer who drove the defendant to the police station testified that he smelled alcohol on the defendant’s breath.
Police officers who were present at the first interview testified that the defendant appeared sober, aware, and alert throughout the questioning.
Again, the police officers testified that the defendant did not appear to be under the influence of alcohol or drugs.
“The second element the Commonwealth must prove beyond a reasonable doubt is that the killing was committed with deliberate premeditation. For the Commonwealth to prove deliberate premeditation, you must *453conclude that the defendant thought before he acted, that is, the defendant formed a plan to murder after deliberation. The element of deliberation, however, does not require an extended time span; nor does it mean that the deliberation must be accomplished slowly; rather, it refers to the purposeful character of the premeditation. If in view of the speed with which the mind can act, the law does not attempt to set any time limit on the time. Deliberation may be a matter of days, hours or indeed, seconds. First the deliberation and premeditation, then the decision to kill, and lastly, the killing in furtherance of that decision.
“All of this may occur within a few seconds. However, it does not exclude action that is taken so quickly that there is no time to think about the action and then determine to do it. Although no particular length of time is required to prove deliberate premeditation, the Commonwealth must show that the defendant’s resolve to kill was the product of cool reflection.
“In this case you have heard evidence that the defendant may have been suffering from a mental impairment at the time he allegedly performed the acts in question because of alcohol and/or drugs. And it’s for you and you alone to say what the evidence reflects. If there is evidence that the defendant had impaired mental capacity because of alcohol or drugs at the time the crime was committed, you should consider what effect, if any, the defendant’s mental impairment had on his ability to deliberately premeditate. You should weigh the defendant’s mental impairment, if any, in evaluating any evidence that he formed a plan to kill the victim after deliberation and reflection.
“The Commonwealth does not have to prove that the defendant was entirely free of mental impairment, but the Commonwealth does have to prove that the defendant was so impaired that he lost the ability to deliberately premeditate. The Commonwealth must prove to you beyond a reasonable doubt that the defendant had the capacity for deliberate premeditation and he did deliberately premeditate.”
The Commonwealth suggests that the word “excludes” is a transcription error and should read, “includes.” We think it more likely that the word “not” may have been incorrectly transcribed because there was no objection to such an obvious error and because with “not” omitted the instruction closely tracks the language approved in Commonwealth v. Callahan, 401 Mass. 627, 633 (1988). Cf. Commonwealth v. Bourgeois, 391 Mass. 869, 884 (1984).
The judge reinstructed the jury as follows:
“You will recall, members of the jury, that I instructed you in first-degree murder and deliberate premeditation. I explained to you what deliberate premeditation was. And I don’t recall whether or not I misspoke or not, but I want to make it crystal clear that the burden in this case to prove that the defendant deliberately premeditated the killing in this case is on the Commonwealth. The Commonwealth has that burden of proof, and that burden of proof must be sustained beyond a reasonable doubt.
“The burden in all of these elements, all of the elements, are [szc] always on the Commonwealth. They must prove each and every element of any of the offenses or all of the offenses I mentioned to you and they must maintain that, and I instructed you on what reasonable doubt is.”
The Commonwealth argues that the misstatement was harmless because there was very little evidence of intoxication. While it is true that several witnesses testified that the defendant appeared sober and alert on the day of and the days following the murder, there was also evidence of drug and alcohol use which warranted the judge’s instructions on mental impairment. This evidence included: testimony of the taxicab driver who drove the defendant from the mall to near his home on the day of the murder that he appeared to be “working off one”; testimony of the police officer who picked up the defendant at his house on the day of the murder that he smelled alcohol on the defendant’s breath; testimony of another police of*456ficer that the day after the murder, the defendant, while following the officer to the police station, was driving slowly and weaving in such a way that the officer would normally have stopped him to investigate for drunk driving. In addition, there was evidence that the defendant was arrested for driving while intoxicated in New York State, three days after the murder; and the defendant was an alcoholic and drug abuser who had been in treatment centers in the past.
The judge listed the factors set out in Commonwealth v. Cunneen, 389 Mass. 216, 227 (1983), but then added, “Extreme atrocity, however, is not limited to cases with such evidence.”
The judge instructed the jury as follows:
“You have also heard testimony during the course of this trial about statements allegedly made by the defendant concerning the offense which is charged in this case.
“Before you may consider any such statements made by the defendant, you’re going to have to make a preliminary determination whether it can be considered as evidence or not. You may not consider any such statements in your deliberations unless from all the evidence in the case the Commonwealth has proved beyond a reasonable doubt that the defendant made the statement that he is alleged to have made and that the statements were made voluntarily, freely, and rationally.
“In your deliberations you may not consider any statements that the defendant made about the offense unless the Commonwealth has proven be*457yond a reasonable doubt both that the defendant made the statement, and that he made it voluntarily, freely, and rationally.”
The defendant did not testify at trial, so the audio- taped interviews with the reporter, although brought in as part of the Commonwealth’s case, provided the only evidence of self-defense.
Dbfbnse counsel: “Did you. and your mother ever have any confrontations or arguments?”
The prosecutor: “I object.”
The judge: “Where are you going with that?”
Defense counsel: “If we may approach.”
“ . . . (Side bar conference.)”
Defense counsel: “Your honor, according to some information I have received, Mrs. Kosilek was known to hit her son on occasion. Now, I can ask that question directly, but I think it’s relevant to show she does react — she did react with some violence on occasion.” •
The judge: “Because she slapped —”
Defense counsel: “Her son. That there had been incidents where she had reacted with some violence.”
The prosecutor: “I don’t know where she’s going. Shé wants the jury to — if that was true that she slapped the defendant — a mother might discipline her child. I don’t know what the answer is in this particular case, though a slap is hardly evidence that the victim in this case attacked the defendant.”
The judge: “It should be more than just a parent slapping a child. I don’t see the relevancy of that. I’m going to sustain the objection at this time.”
The judge’s instructions made clear that the credibility of witnesses was for the jury.