Contrary to his pleas, appellant was convicted by a general court-martial of attempted rape, sodomy, assault, unlawful entry, indecent assault, and communicating threats, in violation of Articles 80, 125, 128, 130, and 134, respectively, of the Uniform Code of Military Justice (UCMJ), 10 U.S.C. §§ 880, 925, 928, 930, and 934. Officer and enlisted members awarded a sentence of confinement at hard labor for seven years, total forfeitures, reduction to pay grade E-l, and a bad-conduct discharge, which was approved on review below by the officer exercising general court-martial jurisdiction.
This case is now before us for review pursuant to Article 66, UCMJ, 10 U.S.C. § 866. Appellant assigns three issues as error, asserting that (1) trial defense counsel provided ineffective representation, (2) the military judge erred in not sua sponte instructing the members on the testimony of an expert witness, and (3) he was denied due process of law by the admission of evidence expressed in terms of mathematical probability. We disagree and affirm.
The offenses resulting in the conviction presently under review occurred during the early morning hours of Saturday, 22 August 1981, at Naval Communications Station, Harold E. Holt, Western Australia. The victim, HM3[C], testified at trial that sometime after she had retired to her quarters at approximately 0100 that morning she was awakened by a man who produced a knife and ordered her not to scream. According to her testimony, she was then “bound and gagged” by the intruder, who attempted to rape her and, after failing to achieve an erection, proceeded to forcibly sodomize her. The victim, who is white, described the assailant as black and muscular, with a beard and moustache, and hair longer than permitted by service regulations. She also detected the odor of alcohol on the assailant’s breath and, in managing to escape, switched on the light, which enabled her to get a “very good look” at his face. As she left the room the assailant pleaded with her not to report the incident.
HM3[C], however, immediately phoned base security. BT2 Francis LeBlanc responded within minutes of the call, finding the victim in a “very agitated and excited state.” She provided him with a description of the assailant consistent with that set forth in her testimony above. They returned to her room so that she could dress. BT2 LeBlanc then escorted the victim to the dispensary where she was examined by LCDR Robert L. Buckley, senior medical *730officer at Harold E. Holt. HM3[C] briefly described the assailant and related the events that had just occurred. From LCDR Buckley’s testimony, it is apparent that her recollection at that time is consonant with her testimony at trial. LCDR Buckley obtained the evidence required by the “rape investigation kit” and noted that the victim’s right wrist was red and that a piece of cloth, which had originally been used as a “gag,” remained tied around her neck.
On Sunday, 23 August 1981, HM3[C] observed appellant walking on base and recognized him as the man who had attacked her the previous morning. She informed a security officer of this observance, also indicating that she now believed the assailant’s last name to be “Jefferson.” In conversation the following evening, HM3[C] offered a description of the assailant to SN Kathy Price, who replied that the individual she described could only be one “Nathaniel Jefferson.” Upon hearing appellant’s name, HM3[C] remembered a brief conversation that she had with him in the chow hall earlier that week. Appellant, who later testified in his own defense, stated that he had no recollection of this conversation. It was elicited during cross-examination of the victim that she and appellant may have had personal contact on two other occasions because she was on duty and signed the log for two antabuse treatments appellant received in July 1981.
In addition to the victim’s unequivocal identification of appellant as the assailant, significant circumstantial evidence was admitted which tends to substantiate the allegations against him. It was established that appellant performed maintenance duties in the BEQ where the victim was berthed and that he had access to the keys to her room. This is important because testimony indicated that the victim’s door locked automatically when closed and that there were no signs of forcible entry into the room. Furthermore, it appears from the victim’s testimony that it would have been impossible to enter the room through the window.
The demographic situation where the instant offenses were committed also points to appellant as the assailant. Harold E. Holt is a small communications station consisting of only about 300 personnel, of which, according to testimony, approximately 30 are black males. Witnesses presented at trial stated that they knew of only a handful of black servicemen stationed there who wore beards and none, with the exception of appellant, with hair in violation of regulations. The base is located in a virtually uninhabited desert area, ruling out the possibility that an Australian citizen may have committed the offenses. These factors, coupled with the victim’s description of the assailant, resulted in a unanimous consensus among the witnesses at trial that the individual described was, indeed, appellant.
The Government concluded its case-in-chief with the expert testimony of CW02 Phillip R. Mills, U.S. Army, a forensic serologist, who stated that he examined pubic and head hairs taken from the victim’s nightgown and a piece of cloth employed in the perpetration of the instant offenses and, after comparing them with samples provided by appellant, opined that they were similar to appellant’s pubic and head hairs. CW02 Mills further testified, over defense objection, that there was a one-in-900 chance that the pubic hairs found on the above items were not appellant’s and a one-in-4500 chance that the head hairs recovered thereon did not belong to appellant. Seminal stains analyzed by CW02 Mills proved inconclusive as to whether they originated from appellant.
Appellant took the stand to deny any involvement in the instant offenses. The record of trial indicates that appellant was prepared to raise an alibi defense. However, the defense was not asserted because the alibi witness’s commanding officer informed investigators that the witness was on duty at the time the instant offenses were committed. The defense also appears to have conducted a trial strategy aimed at convincing the members that HM3[C] fabricated the offenses charged or, in the very least, that her implication of appellant was *731based upon her knowledge that appellant was at Harold E. Holt on a legal hold status awaiting trial in Perth, Western Australia, on another attempted rape charge.1 The assailant in that case, which was under the jurisdiction of the Australian authorities, fit a description similar to that of appellant and, as in the instant case, had been drinking and failed to achieve an erection. The Government, however, presented evidence establishing that the victim did not know about appellant’s pending trial in Perth and that, even if she did, there was no possibility that she could have known the details surrounding that offense.
The three errors assigned present issues which cause us serious concern and require careful examination to assure that appellant received a fair trial. We have elected to address the assignments in reverse order.
I
Appellant’s assertion that he was denied due process is based upon probability evidence admitted through the testimony of CW02 Mills. We conclude, however, that the admission of the challenged evidence was not error and, under the facts and circumstances of this case, nonprejudicial.
Preliminary questioning of CW02 Mills elicited extensive qualifications as an expert in the field of forensic science. At the time of trial, CW02 Mills was a forensic serologist, stationed at U.S. Army Criminal Investigation Laboratory, Camp Zama, Japan, who had conducted “thousands” of microscopic comparisons of hair samples over a period of about 10 to 12 years. His experience was augmented by impressive educational and professional credentials.
As noted earlier in this opinion, CW02 Mills testified that he conducted microscopic comparisons of pubic and head hairs taken from the victim’s nightgown and a piece of cloth employed in the perpetration of the instant offenses with pubic and head hair samples provided by appellant. He was certain that the hairs recovered from these items were of negroid origin. He was also of the opinion that, not only were the pubic and head hairs taken from the crime scene similar to the hair samples provided by appellant, but that there was a one-in-900 chance that these pubic hairs did not originate from appellant and only a one-in-4500 chance that these head hairs did not belong to appellant. The admission of this probability evidence was objected to at trial and now constitutes the basis of appellant’s due process challenge at the appellate level of review.
We initially find that the Government established an adequate foundation for the admission of the expert testimony offered by CW02 Mills, including that which was expressed in terms of mathematical probability. A prerequisite to the admission of scientific evidence is that the principles upon which it is based “must be sufficiently established to have gained general acceptance in the particular field to which it belongs.” United States v. Hulen, 3 M.J. 275, 276 (C.M.A.1977), quoting Frye v. United States, 293 F. 1013, 1014 (D.C.Cir.1923). MIL.R.EVID. 702 may broaden this test, as the rule permits the admission of expert testimony whenever it serves to aid the trier of fact. Cf. United States v. Martin, 13 M.J. 66, 68 n. 4 (C.M.A.1982). The effect of MIL.R.EVID. 702, however, has no bearing on this case because the studies from which CW02 Mills derived his opinion have received sufficient scientific recognition to permit their use in his testimony under the pre-rule application of the Frye test. Courts examining the use of mathematical probability in conjunction with an expert’s testimony concerning the results of hair analysis have had no difficulty with the admissibility of such evidence on the ground that the underlying principles were not generally accepted in a pertinent scientific field. See United States ex rel. DiGiacomo v. Franzen, 680 F.2d 515 (7th Cir.1982); State v. Clayton, 646 P.2d 723 (Utah 1982); State v. Carlson, 267 N.W.2d 170 (Minn.1978). In State v. Carlson, supra, the court went as far as to state that the studies relied upon by the expert testifying in *732that case, which comprise the same data that formed the basis of CW02 Mills’ testimony, were of “unquestioned validity.” Id. at 176. It is also clear from the record that CW02 Mills was qualified to provide the challenged expert testimony and that he employed proper procedures in the microscopic analysis which gave rise to that testimony.
The defense brings to our attention the existence of an article which criticizes the studies relied upon by CW02 Mills. However, the admissibility of expert testimony is not affected by a lack of “absolute certainty of result or unanimity of scientific opinion.” United States v. Baller, 519 F.2d 463, 466 (4th Cir.), cert. denied, 423 U.S. 1019, 96 S.Ct. 456, 46 L.Ed.2d 391 (1975). Of course, the article would go to the weight of CW02 Mills’ testimony.
The admissibility of expert testimony has long been a troublesome area of the law. It is generally agreed upon that limitations on the admission of such evidence are to be left to the sound discretion of the trial court and that the decision to permit expert testimony is to be sustained unless manifestly erroneous. E.g., Garrett v. Desa Industries, Inc., 705 F.2d 721 (4th Cir.1983); United States v. Carson, 702 F.2d 351 (2d Cir.), cert. denied, — U.S. —, 103 S.Ct. 2456, 2457, 77 L.Ed.2d 1335 (1983); United States v. Hensel, 699 F.2d 18 (1st Cir.), cert. denied, — U.S. —, 103 S.Ct. 2431, 77 L.Ed.2d 1317 (1983). However, the undue weight sometimes afforded expert testimony by the trier of fact necessitates a closer examination of its admissibility and, under certain circumstances, the reversal of a judge’s decision permitting its admission. As stated by the Circuit Court in United States v. Baller, supra at 466:
There are good reasons why not every ostensibly scientific technique should be recognized as the basis for expert testimony. Because of its apparent objectivity, an opinion that claims a scientific basis is apt to carry undue weight with the trier of fact. In addition, it is difficult to rebut such an opinion except by other experts or by cross-examination based on a thorough acquaintance with the underlying principles.
These concerns are exacerbated when the evidence admitted not only takes the form of expert scientific testimony but is expressed as mathematical probability. Such situations require an even more critical examination as the danger arises that the trier of fact may be overwhelmed by the evidence and, if the evidence is improperly admitted, “mesmerized” to such an extent that its admission results in substantial prejudice to the accused. See People v. Collins, 68 Cal.2d 319, 66 Cal.Rptr. 497, 438 P.2d 33 (1968). Even when properly admitted, such evidence may infringe upon the accused’s right to a fair trial. As the Supreme Court of Minnesota has observed:
Our concern over [probability] evidence is not with the adequacy of its foundation, but rather with its potentially exaggerated impact on the trier of fact. Testimony expressing opinions or conclusions in terms of statistical probabilities can make the uncertain seem all but proven, and suggest, by quantification, satisfaction of the requirement that guilt be established “beyond a reasonable doubt.” See, Tribe, Trial by Mathematics, 84 Harv.L.Rev. 1329. Diligent cross-examination may in some cases minimize statistical manipulation and confine the scope of probability testimony. We are not convinced, however, that such rebuttal would dispel the psychological impact of the suggestion of mathematical precision, and we share the concern for “the substantial unfairness to a defendant which may result from ill conceived techniques with which the trier of fact is not technically equipped to cope.” People v. Collins, 68 Cal.2d 332, 66 Cal.Rptr. 505, 438 P.2d 41.
State v. Carlson, supra at 176 (footnote omitted).
We likewise recognize the potential prejudicial effect probability evidence may have on a criminal accused. However, we are convinced that, in most cases, members— who generally are more experienced and mature than their civilian counterparts— *733have the ability to give such testimony the appropriate weight. Cf. State v. Clayton, supra at 727 n. 1. Our inquiry, therefore, must focus on whether the challenged testimony was admitted in a prejudicial manner constituting a denial of due process. Since we have already found that a proper foundation was established for the admission of this testimony, we shall confine our due process examination to the cross-examination of the expert witness, the military judge’s comments thereon, and pertinent portions of the Government’s closing argument. Cf. United States ex rel. DiGiacomo v. Franzen, supra; United States v. Massey, 594 F.2d 676 (8th Cir.1979).
At the conclusion of the direct examination of CW02 Mills, trial defense counsel initiated what proved to be an effective cross-examination of the witness. The questioning included the following colloquy:
Q. Does those negroid hairs that you testified to, are they [appellant’s]?
A. I gave the____
Q. Yes or no, can you answer that question? Are they his hairs?
A. No, I cannot say they are his.
Q. Okay. Okay. All you can say is that there is one chance in 900 that they’re his hair? Can you say that with, you know, no — without holding anything back?
A. Yes, sir, I can.
Q. So a one chance in 900 that they’re his hair?
A. Yes, sir.
Q. So the best you can say about the hairs is they may have come from him-— in one in 900 chance they may have come from him?
A. Yes, sir.
(R. 278;279). While obviously not the most eloquent advocate, trial defense counsel, in the presence of the members, elicited the expert’s acknowledgement that he could not conclusively testify that the hair found at the crime scene originated from appellant. Furthermore, trial defense counsel, in his questioning of the witness, misstated the probability evidence previously admitted. However, any confusion resulting therefrom was clarified by the Government on direct and by the following questioning from the military judge:
Q. Well let me perhaps further explain the difficulty I’m having with your saying-only 1 in 900 chance that it’s his hair. I interpret that to mean that if you have 900 people only one of them is going to have a dissimilar hair and the other 899 are going to have similar hairs and that’s not what you’re saying, is it?
A. No, sir, what I’m saying is in a room of 900 people, okay, two people would have hair that are identical. In other words, if you test from 1 up through 800 you’ll test all the way up to 800 or 900 before you find someone else’s hair that are similar to, let’s say that number one man.
Q. Okay. Now, you have told us your results that you reach based on the hair samples that you received in September that’s — and comparing the known samples with the suspect hairs.
A. That’s based on both samples, sir, that was received in September and April.
Q. Okay. So your 1 in 900 and 1 in 4,500 figure is based on the hairs you received in September and the hairs you got a couple of days ago?
A. Yes, sir.
(R. 280-81).
The Government’s closing argument consumes about thirteen pages of the record of trial. Included within that summation is the following reference to the expert testimony of CW02 Mills:
The government would assert that— would urge you to consider, and it’s very important in this case, what Chief Warrant Officer Phillip Mills, a forensic chemist with ten years experience, told you about yesterday. One thing that the accused didn’t count on in this case is that he, like every other human being, sheds pubic and head hairs, whenever that portion of his body is unclothed. Of course he wasn’t concerned about submitting a *734few head hairs. Who, that isn’t exposed to forensic chemistry or law enforcement, criminal detection, would think that, when there wasn’t any struggle, that a number of head hairs would be left behind. And he consented to pull out a few, a few of his own selection. But look at the evidence. Peppered all over this room, in her nightgown, in her bedding, in this braid, were the signs and signature of the accused. Now the government’s not going to try and stand here and tell you that Mr. Mills told you positively that that was the accused’s hairs. Well let’s just look at what Mr. Mills told you. What he said was, those hairs were unique. The unknown hairs found in the bedding, compared to the hairs submitted by the accused, both at the time of the offense, and on 7 April, had many, many qualities in common. What Mr. Mills told you first — first he talked about pubic hairs and then he talked about head hairs. Pubic hairs, he said, are not as unique as head hairs. They’re not exposed to light. They’re not subject to the kind of variations in cuttings and clippings that head hairs are. So for pubic hairs, what he told you was that, in order to be able to get another completely uninvolved person with the same number of characteristics in his hairs, as the hairs found — submitted by the accused, and the ones in the bedding, what you’d have to do is march 900 negro people into that room, and have them all shed their pubic hairs. Then and only then, statistically, would there be a chance that one other man could submit — one other person could submit the same hairs. But the government asks you not to stop at that conclusion. The more compelling conclusion of the two by Mr. Mills, was that the head hairs submitted by the accused matched, or were very similar, to the head hairs of unknown origin found in the bedding, in the cloth and the nightgown of the victim. And what Mr. Mills told you is, although he will not give a positive identification, because forensic science will not permit him to do so, is statistically — for the — in order to have an unknown person match the head hairs submitted by the accused, and the head hairs found in that room on that night, you’d have to march 4500 negro people into that room and have all 4500 of them shed their head hairs. And that’s only of a few head hairs found from that bedding. The government would certainly urge you to consider that that is a signature piece left by the accused.
(R. 379-80). The Government again brought CW02 Mill’s testimony to the attention of the members during rebuttal:
Now Mr. Woodley has come up with some razzle-dazzle figures for all the black people on earth. Unfortunately the accused was stationed at Harold E. Holt, one of the most desolate places on earth. There aren’t millions and millions of black people there. There are only thirty. Only five with a beard. The accused’s hair matches. You got to have 4500 people, statistically, in that room, before you’d find a match to that degree with the accused. Again, his signatures’ all over everything.
(R. 399).
The above excerpts from trial counsel’s closing and rebuttal arguments reflect a proper statement concerning the probability evidence admitted in the instant case. She did not confuse the members by erroneously identifying the hairs recovered from the crime scene with the perpetrator of the offenses. Thus, coupled with the establishment of a sufficient foundation for the challenged testimony, this case is distinguishable from United States v. Massey, supra, relied upon by appellant. As that decision was explained in United States ex rel. DiGiacomo v. Franzen, supra:
In reversing the conviction, the Eighth Circuit held that not only had the Government failed to establish a proper foundation for these mathematical conclusions, but in his closing argument the prosecutor had confused the identifica*735tion of the hair found in the ski cap with the identification of the perpetrator of the crime.... Because of this confusion by the prosecutor and the potential for confusion already inherent in such evidence, the court concluded that plain error had been shown.
Id. at 517.
We, therefore, hold that appellant’s due process rights were not infringed upon by the admission of the expert testimony in the instant case. Accordingly, the assignment of error is rejected.
II
Appellant asserts in his second assignment that it was error for the military judge not to have sua sponte instructed the members on the expert testimony of CW02 Mills. Trial defense counsel, however, did not request such an instruction which, under the circumstances of this case, waived appellant’s right thereto.
Errors in a military judge’s instructions are generally waived if not objected to at trial. E.g., United States v. Grandy, 11 M.J. 270 (C.M.A.1981); United States v. Salley, 9 M.J. 189 (C.M.A.1980). Likewise, the absence of a request by trial defense counsel for a specific instruction precludes appellate consideration of the accused’s right thereto unless the judge’s failure to provide the instruction sua sponte constitutes “plain error.” See United States v. Lell, 16 U.S.C.M.A. 161, 36 C.M.R. 317 (1966). The Court of Military Appeals, quoting from a brief submitted by the Government to that Court, has recently defined plain error as follows:
Plain error is not the equivalent of obvious error. Rather, “... plain error is only found in exceptional circumstances where the reviewing court finds that reversal is necessary to preserve the integrity and reputation of the judicial process, or to prevent a miscarriage of justice (citation omitted)”. United States v. Sims, 617 F.2d 1371, 1377 (9th Cir.1980).
United States v. Webel, 16 M.J. 64, 66 (C.M.A.1983). While the better practice would have been for the military judge to have sua sponte instructed the members on the limitations inherent in the probability evidence admitted at trial, we do not believe that the judge’s failure to so instruct was reversible plain error in this case. A different result would have been appropriate had the probability evidence played a more crucial role in the conviction of appellant. We are convinced, however, that the members’ findings of guilty were not affected by the testimony of CW02 Mills, but based upon the victim’s direct identification of appellant as the perpetrator of the instant offenses and other circumstantial evidence admitted at trial.
Accordingly, the assignment of error is rejected.
Ill
Appellant argues in this assignment of error that he was denied the effective assistance of counsel because trial defense counsel failed to object to the admission of that portion of CW02 Mills’ testimony which was expressed in terms of mathematical probability and because counsel did not “take affirmative action to rebut said evidence.” Appellant’s Brief at pp. 4-5. Trial defense counsel, however, did object to the admission of the probability evidence, but it appears that appellant is correct in his assertion that counsel had not adequately prepared for the expert testimony that CW02 Mills was expected to provide. This is reflected in the following dialogue between the military judge and trial defense counsel:
DC: Well, the defense would like a — perhaps a court citation of some United States court where this [the admission of probability evidence] is allowable.
MJ: Well, why don’t you cite one? I mean, this is your position, counsel. The witness has testified it is, for ten years. It’s up to you to show this court that it’s not. I have evidence before me that it is, it’s now up to you to refute it. I don’t *736think I need a case citation by somebody____
DC: The party which is presenting the evidence has the burden, upon challenge, to assure that we’re dealing with a well-recognized scientific principle.
MJ: Well, my answer, counsel, I think they have presented evidence that it is. I’m persuaded that it is, you have the— you can now persuade me it’s not. I’ll give you that opportunity.
DC: I cannot at this time, your Honor. I haven’t even been given a citation as to any kind of an article which I could read which I could even cross-examine this man on.
MJ: Well, I don’t know that you — anybody had to give you a citation. You have — you have some duty to go out and find this stuff.
(R. 261-62).
The right to effective assistance of counsel entitles an accused to a reasonably competent lawyer who exercises that competence in his client’s behalf throughout the criminal proceeding. United States v. Rivas, 3 M.J. 282 (C.M.A.1978). Effective representation includes a full investigation of the facts and circumstances giving rise to the offenses of which the accused is charged. See United States v. Palenius, 2 M.J. 86, 90 (C.M.A.1977). To prevail on an assertion of ineffectiveness of counsel an accused must demonstrate serious incompetency on the part of his attorney and that the incompetency affected the outcome of the trial. United States v. Jefferson, 13 M.J. 1 (C.M.A.1982); United States v. Mons, 14 M.J. 575 (N.M.C.M.R.1982).
With the above guidance in mind, we are satisfied that appellant received effective representation from trial defense counsel. We do not condone the lack of preparedness demonstrated in the above excerpt from the record, but are of the opinion that it did not effect the outcome of the trial. As indicated earlier in this opinion, counsel’s cross-examination of the expert witness adequately placed that witness’ testimony in perspective. Furthermore, it is evident that no amount of preparation by counsel could have prevented the admission of the probability evidence.
We note that we were initially concerned with trial defense counsel’s trial strategy, which called for the admission of testimony relating to another attempted rape charge which was pending against appellant at the time the instant offenses were alleged to have been committed. Counsel apparently intended to persuade the members that the victim’s implication of appellant was based upon the earlier charge. Although we are convinced that appellant was not prejudiced under the circumstances of this case, we perceive a danger in a defense initiated admission of evidence concerning an accused’s involvement in misconduct similar in nature to that for which he is presently being tried. We recognize, however, that this may be an accepted trial strategy, see United States v. Bad Cob, 560 F.2d 877 (8th Cir.1977), but advise trial defense counsel to exercise caution in employing such tactics.
After an examination of the record in its entirety, we hold that the overall performance of trial defense counsel was adequate and amounted to competent representation. In so holding, we again observe:
Post-trial dissatisfaction with the reality of a sentence may easily spawn accusations directed at one’s counsel. This Court, however, applies the accepted and appropriate standard of counsel competence with recognition that a counsel’s performance must, of necessity, be the subject of concerned and detailed inquiry. United States v. Rivas, 3 M.J. 282 (C.M.A.1977). That inquiry, however, must be tempered, by anyone aware of the demands of criminal trial representation, with recognition of the salient elements of litigation strategy, strength of the government’s case, perception and appreciation by the defendant of the legal issues involved, and the professional judgment of the counsel, when conducting an evaluation of the performance of a crimi*737nal trial advocate. Often these elements will coalesce, sometimes they become discordant and competing priorities. It is the responsibility of the counsel to resolve these priorities to the best interests of his client, within the ethical constraints of his profession and when sufficiently consonant with his or her professional judgment to permit continued representation in the case.
United States v. Dyson, 16 M.J. 907, 909-10 (N.M.C.M.R.1983).
We find no error in this case materially prejudicial to the substantial rights of appellant. The findings and sentence as approved on review below are therefore affirmed.
Judges MAY and CASSEL concur.. Appellant was acquitted of that offense prior to standing trial for the instant offenses.