Abrams, J.
Convicted of rape and indecent assault and battery, the defendant appealed to the Appeals Court. A divided panel of the Appeals Court determined that the judge erroneously disallowed the defendant’s peremptory challenge to a black man on the venire where the complainant was black and the defendant white. The Appeals Court ordered a new trial. Commonwealth v. Curtiss, 40 Mass. App. Ct. 350 (1996). We allowed the Commonwealth’s application for further appellate review. We conclude that the trial judge’s deci[79]*79sion to disallow the peremptory challenge should be affirmed. We also conclude that there was no reversible error in the prosecutor’s closing argument. We affirm the defendant’s convictions.
On February 19, 1992, a mentally impaired twenty-nine year old black woman left a local bar with the defendant, David P. Curtiss. According to the victim, the defendant took her to his car, drove to a nearby neighborhood, pulled off her undergarments and sexually assaulted her and committed two acts of forced intercourse. The defendant then drove the victim across the State border and left her in a rural area of New York. After entering a bar and telephoning her sister in Pittsfield, the victim talked with police and said she had been raped. The defendant denied raping the victim, claiming that she had consented.
The Appeals Court concluded that the judge erred by failing to make an initial determination that a prima facie case of impropriety was shown at the time that the peremptory challenge was exercised. We do not agree that this omission was fatal. We conclude that the judge’s comments are sufficient to support his determination to disallow the peremptory challenge.
The peremptory challenge. Jury empanelment occurred over the course of two days, during which time the judge conducted an individual voir dire of prospective jurors at the defendant’s request. The juror whose participation was challenged by the defendant (juror X) was examined on the second day of empanelment. He was the only black person on either panel of potential jurors. Complying with defense counsel’s request, the judge asked juror X about his wife’s employment with the Department of Social Services (DSS) to ascertain whether her employment as a direct care worker might influence his ability to return an impartial verdict. Juror X indicated that he could be impartial. The defendant exercised a peremptory challenge to challenge the juror.
A single peremptory challenge can constitute a prima facie showing that rebuts the presumption of proper use. See Commonwealth v. Fryar, 414 Mass. 732, 738 (1993). Commonwealth v. Harris, 409 Mass. 461, 465-466 (1991). Commonwealth v. Mathews, 31 Mass. App. Ct. 564, 569 (1991). The judge correctly recognized that “the challenge of [80]*80a single prospective juror within a protected class [may], in some circumstances, constitute a prima facie case of impropriety.” Commonwealth v. Fryar, supra.
The judge, on his own initiative, asked defense counsel to “justify [the challenge] with something more than just a peremptory challenge [in] these circumstances.” Defense counsel expressed his concern that juror X would somehow be influenced by his wife’s participation in the DSS which encompassed “people who are very deeply concerned with sexual abuse, and that gives people a particular point of view in those types of cases.” The judge noted that the potential juror himself was not an employee of DSS, that there was no DSS involvement, and that the alleged victim was not a child.
The judge declared that he would “rule that your challenge is inappropriate [in] these circumstances.” He said, “Let me put it this way. I think the circumstances of this case and the fact that two panels, two arrays, and two separate days produced but one black potential juror, eliminates the need for establishing a pattern and requires me to make a judgment as to whether your challenge has a nonracial basis. The fact that this man’s wife works for a department of the [S]tate that investigates, among other things, children victims and family victims, is insufficient to take it out of the area of a potential challenge based on racial grounds. Now, I want to be careful. I’m not accusing counsel of doing something improper in the sense that he should be admonished, but I am sensitive to the need for there to be a racial balance.” Over defense counsel’s objection, juror X was seated and was sworn as a juror.
We begin with the assumption that the exercise of a peremptory challenge is proper. This assumption is rebuttable, however, on a showing that (1) there is a pattern of excluding members of a discrete group and (2) it is likely that individuals are being excluded solely on the basis of their membership within this group. See Commonwealth v. Soares, 311 Mass. 461, 490, cert. denied, 444 U.S. 881 (1979). See also Commonwealth v. Hamilton, 411 Mass. 313, 316 (1991); Commonwealth v. Wood, 389 Mass. 552, 561 (1983); Commonwealth v. Reid, 384 Mass. 247, 254 (1981).
Confronted with a claim that a peremptory challenge is being used to exclude members of a discrete group, the judge must “determine whether to draw the reasonable inference [81]*81that peremptory challenges have been exercised so as to exclude individuals on account of their group affiliation.” Soares, supra at 490. If the judge so determines, the challenging party must give the judge reasons justifying his exercise of a peremptory challenge which “pertain to the individual qualities of the prospective juror and not to that juror’s group association.” Id. at 491. See Batson v. Kentucky, 476 U.S. 79, 94 (1986). The trial judge then decides whether the challenging party has satisfied his burden by determining whether the proffered neutral reasons are bona fide or “sham excuses belatedly contrived to avoid admitting facts of group discrimination.” Soares, supra at 491, quoting People v. Wheeler, 22 Cal. 3d 258, 282 (1978). See Batson, supra at 98.
In Commonwealth v. Burnett, 418 Mass. 769, 771 (1994), we added to the procedure by requiring the judge to make a finding as to whether an initial prima facie showing of impropriety was established and specifically to determine whether the reasons advanced by the exercising party were “bona fide or a mere sham.”1 We did so in an effort to minimize the necessity for lengthy appellate examinations and retrials springing from confusion over jury selection. See Commonwealth v. Green, 420 Mass. 771, 776 (1995). See also Purkett v. Elem, 514 U.S. 765, 768-769 (1995).2 Then, assuming a race-neutral reason is offered, the trial judge has the responsibility to determine whether, despite the justifications given, “purposeful racial discrimination” exists. Id.
Immediately after the defense announced its intent to exercise a peremptory challenge, the judge noted for the record that juror X was the only black juror on either venire panel. He then asked defense counsel to provide him with some justification for the challenge. The defendant proffered the reason that the juror’s wife was employed by the DSS. By [82]
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Abrams, J.
Convicted of rape and indecent assault and battery, the defendant appealed to the Appeals Court. A divided panel of the Appeals Court determined that the judge erroneously disallowed the defendant’s peremptory challenge to a black man on the venire where the complainant was black and the defendant white. The Appeals Court ordered a new trial. Commonwealth v. Curtiss, 40 Mass. App. Ct. 350 (1996). We allowed the Commonwealth’s application for further appellate review. We conclude that the trial judge’s deci[79]*79sion to disallow the peremptory challenge should be affirmed. We also conclude that there was no reversible error in the prosecutor’s closing argument. We affirm the defendant’s convictions.
On February 19, 1992, a mentally impaired twenty-nine year old black woman left a local bar with the defendant, David P. Curtiss. According to the victim, the defendant took her to his car, drove to a nearby neighborhood, pulled off her undergarments and sexually assaulted her and committed two acts of forced intercourse. The defendant then drove the victim across the State border and left her in a rural area of New York. After entering a bar and telephoning her sister in Pittsfield, the victim talked with police and said she had been raped. The defendant denied raping the victim, claiming that she had consented.
The Appeals Court concluded that the judge erred by failing to make an initial determination that a prima facie case of impropriety was shown at the time that the peremptory challenge was exercised. We do not agree that this omission was fatal. We conclude that the judge’s comments are sufficient to support his determination to disallow the peremptory challenge.
The peremptory challenge. Jury empanelment occurred over the course of two days, during which time the judge conducted an individual voir dire of prospective jurors at the defendant’s request. The juror whose participation was challenged by the defendant (juror X) was examined on the second day of empanelment. He was the only black person on either panel of potential jurors. Complying with defense counsel’s request, the judge asked juror X about his wife’s employment with the Department of Social Services (DSS) to ascertain whether her employment as a direct care worker might influence his ability to return an impartial verdict. Juror X indicated that he could be impartial. The defendant exercised a peremptory challenge to challenge the juror.
A single peremptory challenge can constitute a prima facie showing that rebuts the presumption of proper use. See Commonwealth v. Fryar, 414 Mass. 732, 738 (1993). Commonwealth v. Harris, 409 Mass. 461, 465-466 (1991). Commonwealth v. Mathews, 31 Mass. App. Ct. 564, 569 (1991). The judge correctly recognized that “the challenge of [80]*80a single prospective juror within a protected class [may], in some circumstances, constitute a prima facie case of impropriety.” Commonwealth v. Fryar, supra.
The judge, on his own initiative, asked defense counsel to “justify [the challenge] with something more than just a peremptory challenge [in] these circumstances.” Defense counsel expressed his concern that juror X would somehow be influenced by his wife’s participation in the DSS which encompassed “people who are very deeply concerned with sexual abuse, and that gives people a particular point of view in those types of cases.” The judge noted that the potential juror himself was not an employee of DSS, that there was no DSS involvement, and that the alleged victim was not a child.
The judge declared that he would “rule that your challenge is inappropriate [in] these circumstances.” He said, “Let me put it this way. I think the circumstances of this case and the fact that two panels, two arrays, and two separate days produced but one black potential juror, eliminates the need for establishing a pattern and requires me to make a judgment as to whether your challenge has a nonracial basis. The fact that this man’s wife works for a department of the [S]tate that investigates, among other things, children victims and family victims, is insufficient to take it out of the area of a potential challenge based on racial grounds. Now, I want to be careful. I’m not accusing counsel of doing something improper in the sense that he should be admonished, but I am sensitive to the need for there to be a racial balance.” Over defense counsel’s objection, juror X was seated and was sworn as a juror.
We begin with the assumption that the exercise of a peremptory challenge is proper. This assumption is rebuttable, however, on a showing that (1) there is a pattern of excluding members of a discrete group and (2) it is likely that individuals are being excluded solely on the basis of their membership within this group. See Commonwealth v. Soares, 311 Mass. 461, 490, cert. denied, 444 U.S. 881 (1979). See also Commonwealth v. Hamilton, 411 Mass. 313, 316 (1991); Commonwealth v. Wood, 389 Mass. 552, 561 (1983); Commonwealth v. Reid, 384 Mass. 247, 254 (1981).
Confronted with a claim that a peremptory challenge is being used to exclude members of a discrete group, the judge must “determine whether to draw the reasonable inference [81]*81that peremptory challenges have been exercised so as to exclude individuals on account of their group affiliation.” Soares, supra at 490. If the judge so determines, the challenging party must give the judge reasons justifying his exercise of a peremptory challenge which “pertain to the individual qualities of the prospective juror and not to that juror’s group association.” Id. at 491. See Batson v. Kentucky, 476 U.S. 79, 94 (1986). The trial judge then decides whether the challenging party has satisfied his burden by determining whether the proffered neutral reasons are bona fide or “sham excuses belatedly contrived to avoid admitting facts of group discrimination.” Soares, supra at 491, quoting People v. Wheeler, 22 Cal. 3d 258, 282 (1978). See Batson, supra at 98.
In Commonwealth v. Burnett, 418 Mass. 769, 771 (1994), we added to the procedure by requiring the judge to make a finding as to whether an initial prima facie showing of impropriety was established and specifically to determine whether the reasons advanced by the exercising party were “bona fide or a mere sham.”1 We did so in an effort to minimize the necessity for lengthy appellate examinations and retrials springing from confusion over jury selection. See Commonwealth v. Green, 420 Mass. 771, 776 (1995). See also Purkett v. Elem, 514 U.S. 765, 768-769 (1995).2 Then, assuming a race-neutral reason is offered, the trial judge has the responsibility to determine whether, despite the justifications given, “purposeful racial discrimination” exists. Id.
Immediately after the defense announced its intent to exercise a peremptory challenge, the judge noted for the record that juror X was the only black juror on either venire panel. He then asked defense counsel to provide him with some justification for the challenge. The defendant proffered the reason that the juror’s wife was employed by the DSS. By [82]*82requiring defense counsel to explain his reasons, and by consciously providing the record with an explanation for his actions, the judge implicitly recognized that a prima facie showing of impropriety existed.
The judge recognized his responsibility “to make a judgment as to whether [the] challenge has a nonracial basis.” Although defense counsel stated that his peremptory challenge was motivated by nonracial considerations, the judge was entitled to disbelieve him.3 See Commonwealth v. Fruchtman, 418 Mass. 8, 15, cert. denied, 513 U.S. 951 (1994); Purkett, supra at 769; Commonwealth v. DiMatteo, 12 Mass. App. Ct. 547, 553 (1981) (“reason stated was not the real one”). The judge rejected the defendant’s reason stating: “I’m not convinced. I don’t think there’s such a basis.” The judge did not specifically reject the reason given as not a bona fide reason or as a sham. Nevertheless, we think that the judge’s statements taken as a whole support such a determination. Considering the fact that the potential juror himself did not work for the DSS, that there was no DSS involvement, and that the case turned on the issue of consent by an adult, the judge’s comments justify his determination not to allow the challenge.4
“The determination whether the defendant’s explanation of each challenge was sufficient to establish a nondiscriminatory basis was within the judge’s discretion. . . . ‘Sorting out whether a permissible or impermissible reason underlies a peremptory challenge is the function of the trial judge, and we do not substitute our judgment for his if there is support for it on the record.’ ” Fruchtman, supra at 15, quoting DiMatteo, supra at 552. The judge’s comments sufficiently satisfied [83]*83his responsibility to determine whether the reason advanced by the challenging party was “bona fide or a sham.”5
The prosecutor’s closing argument. The defense also claims that reversible error occurred during the course of the prosecutor’s closing argument. We do not agree. The statements regarding mental capacity and the semen samples summarized evidence that had been introduced during the trial and drew logical conclusions based on that evidence. Commonwealth v. Andrews, 403 Mass. 441, 457 (1988). With respect to the claim of vouching, the prosecutor noted that the jurors were the ultimate arbiters whether reasonable doubt was present. He “interjected no extraneous material or belief but expressed the prosecutor’s view of the strength of the evidence. This was proper argument.” Commonwealth v. Smith, 387 Mass. 900, 907 (1983), citing Commonwealth v. Daigle, 379 Mass. 541, 550 (1980), and Commonwealth v. Stone, 366 Mass. 506, 516 (1974). See Commonwealth v. Kozec, 399 Mass. 514 (1987). There was no error.
Judgments affirmed.