1. It was error for the Judge to refuse to instruct the jury on self-defense. See Commonwealth v. Rodriguez, 370 Mass. 684, 692 (1976). "The fact that the evidence may not be of a character to inspire belief does not authorize the refusal of an instruction based thereon . . . . That is a question within the exclusive province of the jury. However incredible the testimony of a defendant may be he is entitled to an instruction based upon the hypothesis that it is entirely true." People v. Carmen, 36 Cal. 2d 768, 773 (1951), cited with approval in Commonwealth v. Campbell, 352 Mass. 387, 398 (1967), and Commonwealth v. Martin, 369 Mass. 640, 644 (1976). Compare Commonwealth v. Houston, 332 Mass. 687, 690-691 (1955). As it is clear that there was some evidence of self-defense, the Commonwealth had the burden of proving beyond a reasonable doubt that the defendant did not act in self-defense, Commonwealth v. Rodriguez, supra at 688-689, and the Judge was required to give an instruction on self-defense (see e.g., id. at 692 n.10) as requested by the defendant. See Commonwealth v. Monico, 373 Mass. 298, 299 (1977). The case of Commonwealth v. Lacasse, 365 Mass. 271, 273-274 (1974), as well as the other cases relied on by the Commonwealth, are clearly distinguishable. 2. As there must be a new trial, we will discuss another contention of the defendant which is likely to arise at the retrial. The defendant claims the Judge erred in refusing to grant his request to inquire into the possible racial prejudices of prospective jurors. See Commonwealth v. Bumpus, 365 Mass. 66, 67 (1974). "The nature and the extent of the examination of prospective jurors lies within the sound discretion of the trial Judge, [citations omitted], subject to statutory provisions (see, in this regard G. L. c. 234, § 28, as amended through [St. 1975, c. 335]), and the constitutional requirement enunciated in [United States Supreme Court cases], and applied in numerous Massachusetts cases." Commonwealth v. Haglund, 4 Mass. App. Ct. 858, 859 (1976). Although we believe that it would have been proper for the Judge to have granted the defendant's request, see Commonwealth v. Lumley, 367 Mass. 213, 216-217 & n.2 (1975), we cannot conclude on this record that it was error to deny it. Commonwealth v. Pinckney, 365 Mass. 70, 73 (1974). See Commonwealth v. Lozano, 5 Mass. App. Ct. 872, 873 (1977); Commonwealth v. Fleurant, ante 846, 847 (1978). See also Commonwealth v. Bumpus, supra at 70.