On November 25, 1989, the bodies of Ngoc Le (older victim) and her fifteen year old daughter Dixie Poulin (younger victim) were found in their basement apartment in Everett. There was evidence that each had been stabbed to death four days earlier and that the younger victim had received blunt force injuries. Jewelry and cash were missing from the apartment.
In the summer of 1990, the police received information that led to the arrest of the defendant and two other men.1 After a long trial in April, 1992, slowed by the need in many instances for the use of interpreters of Vietnamese, the jury found the defendant guilty of murder in the first degree of both the older victim (based on deliberate premeditation and felony murder) and the younger victim (based on the same grounds and on extreme atrocity or cruelty). The jury also found the defendant guilty of armed robbery.
*394The defendant raises numerous issues in his appeal. (1) He challenges the denial of his pretrial motion to suppress a gun that had been seized in his parents’ apartment. (2) He challenges the denial of his motion to suppress statements that he had made to the police that could have been viewed as evidence of consciousness of guilt. (3) He objects to the judge’s limitation on the cross-examination of two important witnesses who testified that the defendant had confessed to the murders and had made various admissions. The defendant argues that these two witnesses, Linh Nguyen and her husband (according to Vietnamese custom) Thinh Trinh, had a bias against him that, in violation of his constitutional rights, the judge prevented him from pursuing. (4) The defendant raises objections to the prosecutor’s closing argument, to several trial rulings, and to the judge’s charge on reasonable doubt.
We affirm the convictions and see no basis under G. L. c. 278, § 33E (1992 ed.), for relief from the convictions of murder in the first degree.
1. Suppression of the gun. The judge did not err in denying the defendant’s motion to suppress a handgun found in a search of an apartment in the Dorchester section of Boston where the defendant’s parents and other family members lived. The gun, introduced in evidence at trial, was important because it was identified as being similar to one that the defendant had had and as a gun that could have inflicted marks found on the skull of the younger victim.
íhe motion judge concluded that the defendant lacked standing because he had not proved, as was his burden (Commonwealth v. One 1985 Ford Thunderbird Auto., 416 Mass. 603, 608 [1993]), that he had an objectively reasonable expectancy of privacy in the place where the gun was found. The defendant made a limited showing of his involvement with his parents’ apartment and may not now rely on facts not presented to the judge as part of the proceedings on the motion to suppress the gun. We shall assume, without deciding, however, that the defendant had standing to challenge the seizure of the gun, and shall conclude that the po*395lice were entitled to seize it, based on the facts found by the judge.
Shortly after sunrise on August 18, 1990, the police entered the apartment pursuant to a “no-knock” warrant that authorized them to search the defendant and a warrant for the defendant’s arrest. The police were seeking a gun believed to have been used in the course of the crimes. They recognized the possibility that other weapons might be found. When several police officers broke into the Dorchester apartment, the first officer into the apartment entered the first room to the left of the front door, where there were three people, two women and a man. There were two mattresses on the floor. The first officer, accompanied by another officer, directed one of the women to get off one of the mattresses and then kicked it over, thereby uncovering the gun.
In such circumstances, involving the attempted execution of a warrant to arrest someone for committing two murders and involving a reasonable belief that weapons might be present on the premises, the police were entitled to act for their own safety. At the time the mattress was kicked over, the apartment had not been secured, and it was not known who was in it. It developed that the defendant was not present. He was arrested that morning pursuant to the arrest warrant at another location. The police were entitled, however, to protect themselves from an apparent risk, and it does not matter that in retrospect that the peril was not as great as it had initially appeared.2
Our conclusion that the officer was entitled to protect himself and his associates from the threat of any readily accessible weapon, before the search of the premises for the defendant was completed and before the apartment’s occupants were immobilized, is supported by the reasoning of Mary *396 land v. Buie, 494 U.S. 325 (1990). In the Buie case, the protective sweep was permissible, even though conducted after the person arrested pursuant to a warrant was in custody, if it was justified by articulable facts that “would warrant a reasonably prudent officer in believing that the area to be swept harbors an individual posing a danger to those on the arrest scene.” Id. at 334. In our case, the concern was weapons — not the possibility that the defendant or some confederate was under the mattress. The relevant safety concerns, however, are similar. In our case, the officer acted “to take reasonable steps to ensure their safety.” Id. The search was limited in scope and occurred at a time when the suspicion of danger had not been dispelled. The officer could not have known whether events in other parts of the apartment might distract him and his colleague, leaving the occupants of the room with access to any weapon under the mattress.
2. Suppression of statements. The defendant challenges the denial of his motion to suppress statements that he made to the police shortly after his arrest. He argues that his Miranda rights were violated. There was no error.
We summarize the judge’s findings and rulings made after he heard the testimony of police officers, interpreters, and the defendant. After an interpreter in Vietnamese repeated Miranda warnings that a State trooper read in English, the defendant signed a card with Miranda warnings written in Vietnamese and said that he knew of his rights.3 The defendant had lived in this country and attended public schools since 1983. The judge concluded that the defendant had an adequate comprehension of English and that he had understood his rights when they were given to him both in English and in Vietnamese. The judge was warranted in finding that the defendant was sober, alert, and responsive during the police interview. The judge was not required to believe the defendant’s testimony that he had requested an attorney after he had received Miranda warnings. The judge concluded *397that, beyond a reasonable doubt, the defendant was adequately advised of his Miranda rights, that he knowingly and voluntarily waived those rights, and that he voluntarily made statements after the waiver.
On appeal, the defendant argues that the Commonwealth’s evidence was insufficient to prove that he waived his right to counsel and his right to remain silent. There was no evidence that, after giving Miranda rights, the police asked the defendant if he wanted a lawyer. The defendant understood that he was entitled to counsel, and the judge was warranted in finding that he did not ask for a lawyer. The law does not require that the police must go beyond the furnishing of Miranda rights and ask a person who understands his or her rights if he wants a lawyer. See Commonwealth v. Corriveau, 396 Mass. 319, 330 (1985).
The defendant exercised his right to remain silent as to certain questions asked of him, and the trial judge excluded those portions of the defendant’s statements from the trial. On the other hand, the defendant volunteered answers to other questions. The defendant thus selectively declined to answer some questions and answered others. The evidence did not require the judge to find as a fact that the defendant was interrogated after he had asserted his right to remain silent. The judge did not err in ruling that the defendant’s constitutional right to remain silent was not violated.4
3. Motive to lie. The defendant sought to show, through cross-examination of Linh Nguyen and Thinh Trinh, that Linh Nguyen’s father had gone to California in early 1990, when Linh Nguyen, Thinh Trinh, and the defendant were there; that while there, and in the presence of other individu-' ais involved in the illegal distribution of drugs, her father had asked the defendant to carry drugs back to Boston; and *398that the defendant had refused. The defendant argued to the judge that he was entitled to inquire into this incident because it supported his argument that the testimony of Linh Nguyen and Thinh Trinh was given in retribution for the defendant’s embarrassing refusal to cooperate. Defense counsel offered the evidence solely on the question of bias and motive to lie.
Linh Nguyen was an important witness for the prosecution because she testified that the defendant admitted to her that he and another man had killed the victims and that he had used a knife to kill people. She also testified that the defendant and the other man had given her jewelry which, the jury could have found, had been taken from the victims’ apartment.
The defendant first raised the subject of the bias and motive to lie of the principal witnesses against him during his cross-examination of Linh Nguyen. The judge held a voir dire hearing. Linh Nguyen said that she could not remember whether her father had been in California in early 1990 when she, Thinh Trinh, and the defendant were there. She had no memory of her father in California asking the defendant to bring narcotics back to Boston. Linh Nguyen’s voir * dire testimony provided no factual basis for the defendant’s asserted grounds of her bias and motive to lie, and the judge was within his discretion in declining to admit her testimony about her failure of memory on the matters raised during her voir dire hearing. Defense counsel then asked Linh Nguyen before the jury whether she had asked the defendant to bring narcotics back for her father. The judge sustained an objection to that question, and the defendant does not specifically challenge this ruling on appeal. Defense counsel established that Linh Nguyen returned from California by motor vehicle with Thinh Trinh, their young son, the defendant, and perhaps two others.
Thinh Trinh was also an important witness for the Corfimonwealth. He testified that, when the defendant saw Linh Nguyen’s mother wearing a necklace taken in the robbery, the defendant told Thinh Trinh not to let her wear it *399“around here.”5 Thinh Trinh testified further that the defendant had told him that he had stabbed the older victim in the chest, had shown him a knife and said, “This is the knife that kill,” and had shown him a gun similar to one in evidence, as to which, as we have said, there was testimony connecting such a gun with impressions on the skull of the younger victim.
During the cross-examination of Thinh Trinh, defense counsel asked whether, before returning from California with the defendant, he had asked the defendant to bring narcotics back to Boston by airplane. The judge sustained an objection to the question, rejecting the defendant’s argument that an affirmative answer would permit an argument that the witness was biased. The judge also declined to allow a question as to whether Linh Nguyen’s father had made a similar request and had been refused. The defendant then made an offer of proof, consistent with the circumstances considered during the cross-examination of Linh Nguyen.6 Unlike the situation during the cross-examination of Linh Nguyen, in which a voir dire hearing was held (which indicated that she had no testimony that would aid the defendant’s bias argu*400ment), here no voir dire hearing was held or requested. We do not know whether Thinh Trinh would have supported any significant part of the defendant’s theory of retribution, beyond his testimony that Linh Nguyen’s father was present in California when he, Linh Nguyen, and the defendant were there.
In his appeal, the defendant argues that the judge erred in limiting his cross-examination of Linh Nguyen and Thinh Trinh, thereby violating his constitutional rights to due process of law and to confront witnesses under the United States and Massachusetts Constitutions. The argument is that he was entitled on cross-examination of these witnesses' to pursue his theory that their testimony was a “retribution-mativoted fabrication” because they testified against the defendant on orders of Linh Nguyen’s father in retaliation for the defendant’s refusal to transport drugs.
The right of a criminal defendant to cross-examine a prosecution witness to show the witness’s bias, and hence to challenge the witness’s credibility, is well established in the common law, in the United States Constitution (Sixth Amendment), and in the Constitution of the Commonwealth (art. 12 of the Declaration of Rights). See Olden v. Kentucky, 488 U.S. 227, 231 (1988); Davis v. Alaska, 415 U.S. 308, 316-317 (1974); Commonwealth v. LaVelle, 414 Mass. 146, 153 (1993); Commonwealth v. Aguiar, 400 Mass. 508, 513 (1987); Commonwealth v. Joyce, 382 Mass. 222, 229 (1981). “A judge may not restrict cross-examination of a material witness by foreclosing inquiry into a subject that could show bias or prejudice on the part of the witness. . . . While a trial judge has discretion in this matter, he or she has no discretion to prohibit all inquiry into the subject.” Commonwealth v. Aguiar, supra. If, on the facts, there is a possibility of bias, even a remote one, the judge has no discretion to bar all inquiry into the subject. Id. See Commonwealth v. Henson, 394 Mass. 584, 587 (1985). A judge does have discretion to limit cross-examination concerning possible bias when further questioning would be redundant. See *401 Commonwealth v. LaVelle, supra at 154; Commonwealth v. Barnes, 399 Mass. 385, 393 (1987).
A defendant who seeks to pursue a subject in an attempt to demonstrate bias must make a plausible showing that the circumstances existed on which the alleged bias is based. See Commonwealth v. LaVelle, supra at 153; Commonwealth v. Quegan, 35 Mass. App. Ct. 129, 132-135 (1993) (no basis for finding relevance of excluded evidence “beyond tenuous, speculative assertion”). Cf. Commonwealth v. Fordham, 417 Mass. 10, 19-20 (1994) (defendant must show a reasonable likelihood that excluded evidence might have had more than minimal value to him).
The defendant’s bias theory was too tenuous to be one that he was entitled to pursue on the record he presented. It depended on a showing that Linh Nguyen’s father, humiliated in front of others in the illicit drug trade and angered by the defendant’s refusal to transport drugs, persuaded his daughter and Thinh Trinh, his son-in-law (by Vietnamese custom), to make false accusations against the defendant (and for some reason against two other persons who were not at all involved in the humiliation). This theory must account for the facts that (a) somehow Linh Nguyen and Thinh Trinh obtained the jewelry stolen from the victims’ apartment and (b) they knew in some way of the victims’ connection with the defendant and the two other men. It also requires acceptance of the idea, as to which no offer of proof was made, that the degree of humiliation and anger was so intense that Linh Nguyen’s father would put his own daughter and son-in-law, the parents of his grandson, in peril by directing them to testify falsely in a case involving murder in the first degree.
In any event, as the voir dire testimony of Linh Nguyen demonstrates, Linh Nguyen was not going to be a source of evidence in support of the defendant’s bias theory. She said that she could not remember whether her father had been in California when she was there with Thinh Trinh and the defendant. The defendant did not ask for a voir dire of Thinh Trinh, which in these particular circumstances was a neces*402sary part of the defendant’s preservation of his rights on the bias issue. The bias theory was too speculative to rest simply on counsel’s offer of proof.7
4. Other issues. We now consider the defendant’s other objections to conduct and rulings in the course of trial, (a) We discuss the denial of one discovery motion. On August 19, 1990, a Boston newspaper article concerning the crimes stated, according to sources, certain facts about the older victim.8 The defendant moved for disclosure of the sources in order to “establish the existence of other reasonable perpetrators of the offense as well as challenge the adequacy of the investigation.” The motion was denied (and a subpoena to the reporter was quashed) before trial. The motion was again denied during trial. The denial of access to the reporter’s confidential sources, based on a balancing of interests, was within the discretion of the two judges who considered the issue.9 See Matter of a John Doe Grand Jury Investigation, 410 Mass. 596, 599-600 (1991).
(b) There was no likelihood of a miscarriage of justice in the admission through redirect examination of Thinh Trinh of testimony that he had given to the grand jury. Substantially all his testimony about what he had told the grand jury could have been admitted through direct testimony because it involved admissions that the defendant had made to him. *403This included the defendant’s statement that one of his co-defendants knew the older victim and knew of her jewelry and cash.
(c) The defendant objects to the judge’s decision to permit an interpreter to act as a substitute when the regular interpreter became ill. The defendant argues that the interpreter was biased against him. The interpreter had acted as an interpreter in the defendant’s police interrogation and as a witness in the hearing on the defendant’s motion to suppress his statements. The judge concluded that the interpreter was not biased. There is no claim that the interpreter was not qualified. The defendant had his own interpreter at counsel table and makes no claim that the interpreter approved by the judge translated incorrectly. There was no error.
(d) The defendant’s objections to the prosecution’s argument to the jury present neither prejudicial error, where there was objection, nor a substantial likelihood of a miscarriage of justice, where there was no objection. This was a hard fought trial, but none of the objections to the prosecutor’s argument requires a conclusion favorable to the defendant.
(e) The judge did not create a substantial likelihood of a miscarriage of justice in using the words “moral certainty” in the course of defining reasonable doubt for the jury. The charge adequately explained and limited the scope of those words. See Commonwealth v. Gagliardi, 418 Mass. 562, 571-572 (1994), cert. denied, 115 S. Ct. 753 (1995).
5. Conclusion. The circumstances of this case do not warrant relief under G. L. c. 278, § 33E.
Judgments affirmed.