Carl Massey was convicted of bank robbery in violation of 18 U.S.C. §§ 2113(a) and (d), receiving a sentence of 12 years. On appeal Massey challenges (1) the sufficiency of the evidence and (2) the prejudicial effect of testimony elicited by the trial court and the prosecutor’s closing argument, relating to the use of microscopic hair comparisons in terms of statistical probabilities. We find that the evidence was sufficient to sustain the conviction but hold that there was prejudicial error in the overall reference to the defendant’s guilt in terms of mathematical probabilities.
On January 18, 1978, at 12:10 P.M. two men robbed the North Shore State Bank in Duluth, Minnesota. Carl Massey, his sister Yvonne Massey, and John Murray were charged in the same indictment with the bank robbery. Yvonne Massey and John Murray plead guilty on the day of trial; only Carl Massey proceeded to trial. The Government’s evidence included pictures recorded by an electronic surveillance camera of two men in the process of robbing the bank. The first man wore a ski mask with one center opening, surgical rubber gloves and a tan field jacket. The second man, wearing a ski mask with openings only for his eyes and mouth, leather gloves over cloth gloves, ragged jeans and a hooded parka, brandished two cocked guns during the course of the robbery.
The two men fled the bank in a beige camper, which the police found abandoned a short distance from the bank. A police dog followed the scent of a track leading from the camper to a spot in a parking lot behind a hardware store, where the dog lost the scent. At approximately noon on the day of the robbery an employee and customer of the hardware store had observed a yellow Volkswagon with its motor running in the same parking lot. A young woman wearing a red scarf and wire rim glasses was observed in the driver’s seat.
At approximately 12:45 P.M. on thé day of the robbery, a witness, George Bowen, looked out his window and noticed a yellow Volkswagon parked in front of 1217 West Fifth Street, the residence of William and Lana Papberg. At about 1:10 P.M. he observed a man with blond hair, wearing a blue vest jacket, come out of the Papberg residence and begin rummaging through the car.
At about 1:14 P.M. Sergeant Eli Miletich observed the yellow Volkswagon parked in front of the Papberg residence. The officer then went to a nearby phone, ran a license check and discovered that the Volkswagon was registered to Nancy Massey, mother of Carl Massey and Yvonne Massey. When he returned after running the license check, the Volkswagon was gone.
At approximately 2:15 P.M. the Volkswagon returned to the Papberg residence. Yvonne Massey was driving; John Murray was a passenger. The couple entered the Papberg residence and stayed for approximately 20 minutes. When they returned Massey and Murray consented to a search of the car. In a suitcase belonging *678to John Murray the officer discovered a red notebook which contained a list of articles intended for use in criminal activity. The notebook also contained the following names and initials and accompanying percentage figures: “Jay, 100. Lana, 250. M.C., 10 percent. Y., 15 percent. C., 25 percent. G., 25 percent. J., 25 percent.” 1 Officers continued surveillance of the Pap-berg residence throughout the afternoon and into the evening.
At approximately 8:30 P.M. the Papberg residence was searched pursuant to a search warrant. Those present during the search included Lana Papberg, Nancy Massey, Yvonne Massey and Carl Massey, who was wearing a blue vest jacket. Among the many items seized in the basement were a ski mask with holes for the eyes and mouth, a red scarf, a pair of wire rim glasses and surgical rubber gloves. One of the bank’s employees testified that the robber holding the guns wore a ski mask that covered everything but his eyes and mouth. There was also testimony that the red scarf and wire rim glasses were similar to the items worn by the woman sitting in the yellow Volks wagon on the day of the robbery. Also seized from the Papberg residence were two jackets, one of which an expert in photographic comparison analysis positively identified as the same jacket appearing in the surveillance photographs. The expert testified that the other jacket was similar to the one pictured by the surveillance camera but he was unable to make a positive identification.
F.B.I. Agent Robert Harvey, who participated in the search of the Papberg residence, found a blue ski mask with a center opening similar to the one described by a bank employee as belonging to one of the robbers. Five hairs found in the ski mask were microscopically compared with hair samples taken from Carl Massey’s head. Agent James Hilverda, an expert in microscopic analysis, testified that Carl Massey’s hair was similar to three of the five hairs found in the blue ski mask in all categories of microscopic comparison.
Two tellers at the bank testified that two days prior to the robbery, a young man with blond hair approached a teller’s window and asked for a roll of quarters and some coin wrappers. Both tellers subsequent to the robbery identified the blond young man as Carl Massey.
In view of the jury verdict in favor of the Government, the evidence, although circumstantial, along with all reasonable inferences to be drawn therefrom, must be reviewed in the light most favorable to the Government. At oral argument the Government conceded, as we feel it must, that the observation of the defendant at the bank two days before the robbery, the notebook, the observation of a young man with blond hair rummaging through the Volkswagon shortly after the robbery and Massey’s presence at the Papberg home at the time of the search are insufficient facts to sustain Massey’s conviction. Although the cumulative effect of this evidence points a strong finger of suspicion it is not in itself *679sufficient to prove that Massey was one of the bank robbers. The linchpin is established, however, when this evidence is weighed with the testimony of the Government’s expert which established that three of five hair samples found in the blue ski mask (similar to the one used in the robbery) matched in all areas of microscopic comparison with known samples of defendant’s hair. We therefore reject defendant’s contention that the evidence was insufficient to support the conviction.
The evidentiary importance of the microscopic comparison of the hair samples, however, requires this court to scrutinize defendant’s challenge to its foundation, the trial court’s interpretation of it and its use by the prosecutor in closing argument.2 F.B.I. Agent Robert Harvey testified that five hairs were found in the blue ski mask. James Hilverda, an expert in microscopic analysis, then testified that Massey’s hair was similar to three of the five hairs found in the blue ski mask in all categories of microscopic comparison. After so testifying the court interrogated Mr. Hilverda and the following colloquy occurred:
THE COURT: How many people in the United States have hair that you couldn’t distinguish? In other words, what’s the likelihood that any one individual, his hair might meet all the characteristics of another individual?
A. Well, first of all you could eliminate people from different races. .
You can say positively it came from a person of the Caucasian race or the Mongoloid race and the Negroid race, so basically exclude all those.
You could exclude primarily those people who have mixed racial origin.
So you can be positive on those.
It’s the type of thing — hair evidence is the type that you can not positively say it comes from one individual to the exclusion of all others.
And I would basically have to go with my experience in examining about probably in excess of 2,000 cases, that I have seen only on a couple of occasions I have seen hair from two different individuals I could not distinguish, that they were so similar, that some hairs within each sample were very close and I did not feel comfortable enough to work the case and to say that one hair came from one individual to the exclusion of the other.
So I did not work the case in that instance.
THE COURT: Two chances — one chance in a thousand?
A. Well that’s very difficult — you’re putting it in probabilities — because I do not take a hair from each case and compare it with hair from all the other cases.
But that’s the frequency with which I have seen it.
The other thing, I could give you a study — the Canadians have done a study where they have come up with one in 4,500, that a possibility that a hair which you have done or matched in the manner which I have set forth, there’s a chance of one in 4,500 these hairs could have come from another individual.
THE COURT: If you have one hair there, and then you could compare it with 4,500 others, and you might find one?
A. You might find one that would show the same. That would be assuming that you took hairs from 4,500 other people of the same race.
Of course, if you had more hairs than that, you would have multiplication factor at that point.
The defendant does not challenge the opinion evidence that certain hairs within the ski mask were microscopically identical to his hair. The fundamental challenge relates primarily to the prejudicial effect of the use of mathematical statistical probabil*680ity as elicited and interpreted by the trial judge and argued by the prosecutor.
The actual testimony of the expert witness is somewhat confusing. It is difficult to understand just what tests he conducted in 2,000 cases because of lack of foundational detail to understand the type of experimentation or studies made. Yet the witness was candid in saying his own experience did not establish a statistical probability. Our reading of the record is simply that in his own experience the witness had microscopically examined 2,000 cases and in only one or two cases was he ever unable to make identification. There is no foundation to show the factual circumstances surrounding each of his examinations and certainly there is no statistical probability which could be drawn from his experience to show that there was only “one chance in a 1,000” that hair comparisons could be in error.
Concerning the witness’ reference to the Canadian study there can be no doubt that the foundation for such testimony was insufficient. The witness testified that he did not know the nature and extent of the studies conducted from which the statistics were gathered. See Bogacki v. American Machine & Foundry Co., 417 F.2d 400, 408 (3d Cir. 1969).
At best, we conclude the court’s colloquy with the witness concerning mathematical probabilities was speculative and confusing. The gravamen of the error came during the trial judge’s comment construing the testimony in terms of the probability of making an erroneous identification through the comparison of hair samples.
However, prejudicial harm arises in the Government’s closing summation, which exacerbated the trial judge’s misunderstanding of the evidence. The prosecutor argued:
I think there was some reference both to his own experience and the experience of a survey conducted by the Canadians as to the accuracy of the conclusions which one can draw from finding hair samples which are microscopically the same. I believe the witness said that out of 2,000 or 2,500 examinations only a handful — I believe he said 3, but let’s say 5 — only a handful of instances occurred where he was unable to distinguish the hair from two different people.3 I believe that it was a handful out of 4,500 in the Canadian test.
Now in order to convict the defendant, you must find him guilty beyond a reasonable doubt.
That is not beyond all doubt, but that is beyond a reasonable doubt.
The Judge will tell you what that is. It is a fair doubt. It is a doubt that would make you hesitate in the more serious of your own affairs.
A handful — S to 5 out of 2,000 — that’s better than 99.44 percent; it’s better than Ivory Soap, if you remember the commercial. It’s very very convincing.
Now hair samples are not like fingerprints. It is not positive identification. There is a theoretical possibility (and it actually happened in the case of this examiner in 3 to 5 times out of say, 2,000) where the hairs of two different heads can look the same when you examine the whole range of their characteristics.
However, it is infinitesimally rare, and when we talk about the range of proof which we can use in deciding questions for us, those kinds of percentages are higher than the percentage we use in any other area I can think of in terms of making a decision.
I submit to you that if hair samples are found — a known and an unknown — and they are microscopically identical, that it is at the very least proof beyond a reasonable doubt that the unknown hair comes from the same head as the known hair.
Now human hairs were found in this ski mask which I am holding, Government’s Exhibit 31, which appears as the ski mask worn by the robber carrying the sack out of the bank and which was found in the same house as the fatigue jacket and the parka.
*681The hair found in the ski mask was examined as to the 15 characteristics, and all 15 characteristics were microscopically the same as the known hair sample of the defendant Carl Massey.
I argue to you that we have presented proof beyond a reasonable doubt that the clothing found in the. Papberg residence was used in the robbery, and we have shown beyond a reasonable doubt that this ski mask was used by the defendant Carl Massey; and, while there is in fact other evidence which corroborates this, including the fact that he cased the bank, for example, we would argue to you that just the hair sample would be proof beyond a reasonable doubt because it is so convincing. (Emphasis added.)
By using such misleading mathematical odds the prosecutor “confuse[d] the probability of concurrence of the identifying marks with the probability of mistaken identification” of the bank robber. McCormick on Evidence § 204, at 487 (E. Cleary ed. 1972). In other words, the prosecutor has infused in the minds of the jury the confusion in identifying the hair with identifying the perpetrator of the crime. As stated in State v. Carlson, 267 N.W.2d 170 (Minn.1978), when reviewing similar opinion evidence:
Our concern over this evidence is . with its potentially exaggerated impact upon 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.” 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.”
267 N.W.2d at 176 (citations and footnote omitted).
See also Miller v. State, 240 Ark. 340, 399 S.W.2d 268 (1966); People v. Collins, 68 Cal.2d 319, 66 Cal.Rptr. 497, 438 P.2d 33 (1968); State v. Sneed, 76 N.M. 349, 414 P.2d 858 (1966).4
In view of the obvious importance of the hair comparison in conjunction with the weakness of the other circumstantial proof, we cannot say the error was harmless.
The judgment is reversed and remanded for a new trial.
. The Government urges that the names and initials correspond to the first names of persons present at the Papberg residence on the night of the robbery: “Lana,” Lana Papberg; “J,” John Murray; “Y,” Yvonne Massey; and “C,” Carl Massey. The notebook also contained the following:
Tuesday. Cars, 8:00 o’clock, 12:00 o’clock, 4:00 o’clock. One run through. Make all radios work. Gather all materials. Sacks for everything. Pick up M-l. Call Greg Monday. Look for cars 8, 12 and 4. One run through. A and E. Map cover. Stop at Jay’s. 9. Folks. Scanner, walkie-talkie, stopwatch, clothes, mask, 357. Mac, lunch late, Lana, Elton, house, antenna, Nancy. Gloves.
On another page, as described by a police officer, was:
[A] drawing, a sketch of some kind with what could be a pot of gold with an arrow, leading to a vehicle, leading to another vehicle, leading to a third vehicle labelled “Safe and Clean”, and another arrow proceeding to a house, and then an arrow proceeding to a, what could be a pot of gold.
The notebook was admissible into evidence. See United States v. Wilson, 532 F.2d 641 (8th Cir.), cert. denied, 429 U.S. 846, 97 S.Ct. 128, 50 L.Ed.2d 117 (1976). However, the incriminating effect of such writings, at least as against Carl Massey, is questionable. Cf. United States v. Brown, 584 F.2d 252 (8th Cir. 1978).
. Since defense counsel did not object to the testimony elicited by the trial court or to the prosecutor’s closing argument this court must review the alleged error in terms of plain error and in terms of whether it affected the substantial rights of the defendant. See Fed.R.Crim.P. 52(b), United States v. Davis, 557 F.2d 1239 (8th Cir.), cert. denied, 434 U.S. 971, 98 S.Ct. 523, 54 L.Ed.2d 461 (1977).
. This, of course, is not what the witness stated.
. Jurors being exposed to statistical probabilities “may find themselves ‘surprised’ at the strength of the inference of guilt flowing from the combination of mathematical and non-mathematical evidence. Indeed they may, and in a far deeper sense than with other equally obscure forms of expert testimony, for such testimony typically represents no more than an input into the trial process, whereas the proposed use of [statistical probability] methods changes the character of the trial process itself. When that change yields a ‘surprisingly’ strong inference of guilt in a particular case, it is by no means clear that, so long as one keeps one’s numbers straight, ‘this . . is no more than the evidence deserves.’ Methods of proof that impose moral blame or authorize official sanctions on the basis of evidence that fails to penetrate or convince the untutored contemporary intuition threaten to make the legal system seem even more alien and inhuman than it already does to distressingly many.” Tribe, Trial by Mathematics, 84 Harv.L.Rev. 1329, 1375-76 (1971) (footnotes omitted).