The opinion of the court was delivered by
Six, J.:
The defendant, Jimmy Jack Searles, appeals from his convictions of felony murder, K.S.A. 21-3401, and attempted rape, K.S.A. 21-3301; K.S.A. 21-3502.
The issues for our review are whether
(1) the trial court improperly allowed the State to comment on Searles’ exercise of his privilege against self-incrimination;
(2) the trial court erred in allowing the prosecution to introduce K.S.A. 60-455 evidence arising from two prior crimes charged against Searles, one of which resulted in an acquittal and the other in a mistrial with no retrial;
(3) the trial court erred in giving a PIK Crim. 2d 52.06 limiting instruction on the K.S.A. 60-455 evidence which stated that evidence had been admitted tending to prove that Searles committed other crimes; and
(4) the trial court erred in admitting the blood analysis testimony of the State’s experts.
We find no error and affirm.
FACTS
The decomposed body of Roxanne G., the mother of three young children, was found beside a county road outside of Par[569]*569sons, Kansas, ten days after her disappearance. An autopsy revealed that Roxanne had died from a blow to the head.
The night she disappeared, Roxanne spent the evening with her neighbor, Midge. They decided to go to Joe’s Club to be with Midge’s husband. Midge’s eldest daughter, Sheila, babysat at Roxanne’s home with her younger siblings and Roxanne’s children. A short time after Roxanne arrived at the club, Jimmy Jack Searles, the defendant, approached her and asked her to dance. After the dance, Roxanne returned to sit with Midge. Roxanne wanted to dance again. Midge suggested that Roxanne ask Searles to dance. Roxanne and Searles had danced several times when Roxanne told Midge that she was leaving with Searles to go to another bar, the Midnight Factory. Midge cautioned Roxanne against leaving with a man she had just met, but Roxanne responded that she would be all right because she would know a hundred people at the Midnight Factory.
Midge noticed it was 11:43 p.m. when Roxanne left with Searles. When Midge arrived home, she noticed Roxanne’s car parked where Roxanne had left it. Midge immediately went over to Roxanne’s apartment. She told Sheila that Roxanne had gone to the Midnight Factory and would be home later.
A couple of hours later, Midge was awakened by Sheila. Roxanne still had not returned home and her three-week-old baby was crying. Midge returned to Roxanne’s apartment with Sheila to find some formula for the baby and then went back to bed. Sheila woke her mother a second time at 7:00 in the morning to tell her that Roxanne had not returned. Roxanne’s brother and his wife came over a few hours later. The police were called later that evening.
The case was initially investigated as a missing persons report. Searles was interviewed by the police. His pickup truck was taken into custody with his consent. Searles told the police that he had gone to Joe’s Club at 7:00 that evening, met and danced with Roxanne, and left with her at approximately 11:05 p.m. Instead of going directly to the Midnight Factory, Searles took Roxanne to a friend’s house. The friend, Jim Lane, confirmed that Searles and a woman introduced as Roxanne came to his house late that night. According to Lane, Searles arrived shortly after midnight to talk to him about a combine they owned together and left [570]*570approximately an hour later. Searles stated that after they left Lane’s house, he decided he did not want to go dancing. He said he dropped Roxanne off at the Midnight Factory before returning home to his wife.
The Midnight Factory was under surveillance that night. A special agent for the Kansas Bureau of Investigation (KBI) was working on an undercover investigation at the club. She was inside to observe and to attempt to purchase narcotics. She was at the club until 1:45 a.m. but did not see Roxanne. None of the officers stationed in various places outside saw Roxanne dropped off at the Midnight Factory by Searles. However, the officers testified that the club was very busy and many vehicles, including pickup trucks similar to the one Searles drove, pulled into the parking lot that night. They did not notice anyone being dropped off outside the club, although such a drop-off would have been unusual enough that they thought they would have remembered it.
Ten days later, the body of a deceased female was found in a weed-filled ditch about fifteen feet from a gravel road in Labette County. The body did not appear to have been moved. It was decayed and had been damaged by animals. The body was propped up with the buttocks partly in the air and appeared to have been in that position for some time. According to the county coroner, who had been summoned to the scene, he had to use a flashlight to see the body. He saw no garments on the body, with the exception of a piece of an undergarment that appeared to be ripped on one thigh. The sheriff, however, testified that a shirt was found on the body in the vicinity of the neck.
In the coroner’s opinion, a violent sexual act had occurred, as well as a murder. This opinion was based upon the fact that the deceased was a young female with her clothing removed and upon the position of the body. The coroner said that, based on his experience, even when a body remains exposed for prolonged periods of time “the articles of clothing do not simply come off, do not become removed spontaneously.”
Dr. William Eckert, a forensic pathologist from Wichita, viewed the scene. The body was taken to Wichita for an autopsy. Dr. Eckert determined the body was Roxanne’s by a comparison of the teeth with Roxanne’s dental records.
[571]*571The examination of the body was limited due to the advanced state of decomposition and the damage done to the body by animals. It was not possible to perform medical tests to see if there was semen or sperm in the vagina or rectum. However, Dr. Eckert was able to determine the cause of death to be a skull fracture caused by a blunt instrument. Dr. Eckert observed that there was a curve to the fracture which would suggest that the object used to make the fracture had a curve to it. Dr. Eckert also concluded that a lug wrench found in Searles’ truck could have made the curved indentation on the skull. Finally, he concluded that, although the exact time of death could not be determined, the state of decomposition of the body was consistent with the period of time Roxanne was last seen alive.
Shortly after the autopsy, Searles’ truck was searched a second time. During the initial search of the truck the officers had seized several tools, including a lug wrench and a section of rope and wire. The second search of the truck was conducted by a KBI agent who used luminal to search for blood on the truck. Luminal is a chemical that reacts with blood and is used on metal, fabric, and wood to help locate blood or blood residue. If blood is present the area will glow. The test does not ascertain whether the blood is animal or human.
When the bed of the truck was first sprayed, specific areas glowed indicating the presence of blood. Those areas were between the back of the truck and the left wheel well, along the side wall, and on top of the back bumper. Scrapings were taken and sent to the KBI lab for evaluation. Another search of the truck was conducted. During the third search, more blood was located on the bumper, but this time it was found on the inside or back side of the rear bumper. Again, scrapings were taken.
Searles was interviewed a second time and he was read his Miranda rights. He elected to speak with the police. Searles related basically the same story at the second interview, except he stated that his wife told him he arrived home at 1:30 a.m. instead of between midnight and 12:30 a.m. as he originally thought. Searles also told the officers that he was not attracted to Roxanne. According to the officer, Searles’ demeanor at this interview was very cold and his actions were very calm. Searles’ initial claim of trial error arises from this interview.
[572]*572Eileen Burnau, a criminalist with the KBI, performed tests to identify the genetic marking or blood grouping of the blood found on Searles’ truck, blood taken from Searles, and blood taken from Roxanne’s parents.
More tests on the blood were done by Dr. Edward Blake, a forensic serologist. Blake received several items, including a scraping of blood from the bumper of Searles’ truck, a specimen of hair from Roxanne, three small pieces of bloodstained rope, and blood samples from Searles and from Roxanne’s parents.
STATE’S COMMENT ON POST-ARREST SILENCE
At trial, during the direct examination of Officer Tucker, the State elicited testimony concerning the second interview of Searles. This interview took place at the Law Enforcement Center eight days after the victim’s body had been found and lasted for over three hours. At that time Searles was read his Miranda rights. Searles indicated he understood those rights and agreed to speak with the officers. About three-fourths of the way through the interview, Searles was asked if he had killed Roxanne. According to Officer Tucker, Searles did not respond for a long period of time and finally said no. Searles then asked, “If I did what you say I did, what happens now?” In response, Officer Tucker told Searles that he just wanted to hear Searles’ story of what actually had happened, but no promises or deals could be made. After a long silence, the conversation ended when Searles replied that in that case, “I have nothing to say.” After Tucker related this statement at trial, the State immediately went on to other questions. The fact that Searles had stated, “I have nothing to say,” was never raised again.
Searles first claims that allowing the State to introduce this evidence of his post-arrest/post-Miranda silence was violative of due process of law. Searles admits he did initiate conversation with the police by asking, “What happens now?” He complains on appeal of the admission of his statement, “I have nothing to say. ”
Doyle v. Ohio, 426 U.S. 610, 49 L. Ed. 2d 91, 96 S. Ct. 2240 (1976), held that the State’s use of post-arrest/post-Miranda silence for impeachment purposes was constitutionally impermissible. A Doyle violation occurs when a defendant’s post-arrest [573]*573silence is used to impeach the defendant when an exculpatory explanation is subsequently offered at trial.
We recognized Doyle in State v. Mims, 220 Kan. 726, 556 P.2d 387 (1976). In Mims, we found harmless error when the prosecutor on cross-examination asked the defendant why he did not tell his alibi story to the police at the time of his arrest. Mims’ stories were consistent. He had clearly offered his alibi story to the police at that time.
Recently, in State v. Higgins, 243 Kan. 48, 755 P.2d 12 (1988), we extended the holding in Doyle and Mims. In Higgins, the defendant’s post-arrest silence was first introduced during defense cross-examination of a police detective. The detective testified that, because the defendant would not sign a waiver of his rights, the detective could not obtain a statement from him. On redirect, the prosecution proceeded to question the detective in detail about the defendant’s refusal to speak with him after the defendant’s arrest. The defense objection was overruled on the grounds that the defendant had waived his right to object by introducing the defendant’s post-arrest silence in his cross-examination. Again, in its closing argument, the State commented on the defendant’s silence. While acknowledging that one is allowed to exercise the right to remain silent, the State asked why the defendant had not denied the crime or given an alibi if innocent. We held that, under Doyle and Mims, the testimony concerning the defendant’s post-arrest silence and the State’s comments constituted reversible error. We attached importance to the comments of the prosecutor during closing argument and the emphasis placed on the post-arrest silence.
The United States Supreme Court addressed the scope of Doyle in Greer v. Miller, 483 U.S. 756, 97 L. Ed. 2d 618, 107 S. Ct. 3102, reh. denied 483 U.S. 1056 (1987). In Greer, the majority held that a Doyle violation occurs when a trial court allows specific inquiry or comment on an accused’s post-Miranda silence. If the trial court attempts to cure such conduct through a sustained objection or limiting instruction, the conduct does not violate Doyle but is prosecutorial misconduct which may or may not rise to the level of a due process violation. Greer, 483 U.S. at 764-65.
[574]*574The question about which Searles complains is similar to the situation in State v. Taylor, 223 Kan. 261, 574 P.2d 210 (1977). In Taylor, we stated: “The questioning really had nothing to do with defendant’s silence after arrest and after receiving the Miranda warnings. His silence at that stage was not emphasized and was not used for impeachment purposes contrary to Doyle.” 223 Kan. at 265.
In the present case, where there was only one question concerning Searles’ statement that he had nothing to say and no further comment on his answer, there was no Doyle violation.
Searles also claims the State’s comment upon his privilege against self-incrimination was statutorily impermissible in violation of K.S.A. 60-425 and K.S.A. 60-439. Searles contends that by informing the arresting officers that he would not answer that question, Searles, in addition to asserting a constitutional right, was exercising a statutory privilege “to refuse to disclose in an action or to a public official . . . any matter that will incriminate such person.” K.S.A. 60-425.
K.S.A. 60-439 provides:
“If a privilege is exercised not to testify or to prevent another from testifying, either in the action or with respect to particular matters, or to refuse to disclose or to prevent another from disclosing any matter, the judge and counsel may not comment thereon, no presumption shall arise with respect to the exercise of the privilege, and the trier of fact may not draw any adverse inference therefrom. In those jury cases wherein the right to exercise a privilege, as herein provided, may be misunderstood and unfavorable inferences drawn by the trier of the fact, or may be impaired in the particular case, the court, at the request of the party exercising the privilege, may instruct the jury in support of such privilege.”
State v. Nott, 234 Kan. 34, 669 P.2d 660 (1983), states plainly that K.S.A. 60-439 is limited to a situation where a comment is made on a privilege in the trial where the privilege is asserted. While the State did elicit the fact that at one point Searles stated he had nothing to say, the State did not comment on that assertion. The trial court’s ruling on this issue was correct.
OTHER CRIMES EVIDENCE — K.S.A. 60-455
Prior to trial, the State moved to admit evidence of other crimes pursuant to K.S.A. 60-455, contending that the other crimes were relevant to the issue of identity. At trial the State was permitted [575]*575to present evidence showing that Searles had stood trial for rape in Craig County, Oklahoma, in April of 1980; and that in October of 1984, he had been tried for assault and attempted rape in Montgomery County, Kansas. The Oklahoma case resulted in a hung jury; Searles was not retried. He was acquitted on the Montgomery County charges.
Searles claims error on grounds that the evidence of the prior charges was not relevant to prove a disputed fact. He contends the risk of undue prejudice outweighed the probative value of the evidence. He also argues that the introduction of the other crimes evidence violated his rights under the double jeopardy clause of the Fifth Amendment. Finally, Searles contends that the testimony offered at trial went beyond the evidence proffered at the motion to admit other crimes evidence and was impermissibly prejudicial.
a. P.A.’s Testimony — The Hung Jury Case
At trial, evidence of the Oklahoma incident was introduced through the testimony of P.A. In December 1979, P.A. was 22 years old, divorced, and living in a trailer house with her three-year-old son. P.A. knew Searles, having been introduced to him through her ex-husband. Searles was married and his wife was expecting a child. P.A. had gone to bed about 1:00 a.m. She was awakened later that morning at approximately 3:30 by the sound of breaking glass. She then went to the back door of the trailer house and saw that an arm was stuck through the window trying to reach the door knob.
P.A. grabbed the wrist and asked who it was. Searles said it was Jim and that he needed to talk to her. She recognized Searles’ voice and told him to go to the front door to talk to her there. When P.A. opened the front door, Searles opened the screen door and came in. Searles had been drinking and still had a beer bottle in his hand.
He first sat down and told P.A. he needed to talk to her about his wife. When she replied that he did not need to talk to her, he needed to talk to his wife, he stated that he had really come to make love to her. At that point, P.A.’s three-year-old son started crying. She went to the bedroom, picked him up, and carried him back to the living room.
[576]*576Searles, in the meantime, had gone to the kitchen, opened the back door of the trailer, and vomited outside. He then came back in and sat on the arm of the chair where P.A. was sitting with her son. As she got up to move away from him, he grabbed her arm. Searles threw P.A. to the floor, removed her underwear, and began choking her. Searles raped her as she tried to comfort her son.
The rape stopped when Searles passed out. P.A. left with her son to find help from a friend. Searles was tried for rape the next spring. The case ended in a mistrial. The trial was rescheduled for the following fall. In the meantime, P.A. had moved to Idaho and did not return to Oklahoma for the rescheduled trial. P.A. stated that she did not return because she had already been through enough harassment and humiliation. Instead of being the victim, she said, she had become the villain.
b. T.M.’s Testimony — The Acquittal Case
T.M. testified regarding the Montgomery County incident. T.M. and her daughter were living in Coffeyville, Kansas, with T.M.’s mother, T.M.’s three younger sisters, and a younger brother. At approximately 10:30 p.m. on March 21, 1984, T.M. went out to a local club. While there, she met Searles and the girl with whom he lived at the time, both of whom she already knew. After about an hour, she went to another bar where she was to meet her mother. At the second bar, she again ran into Searles and his girlfriend. At one point in the evening, Searles asked T.M. to meet him at the front door of the club, but she declined. She went home a little after midnight and put on her night clothes and went to bed.
She was awakened later by dogs barking and a pounding and yelling at the front door. A friend, who was sleeping on the couch, told T.M. that it sounded like Searles. T.M. opened the door. When T.M. let Searles in she knew that he had been drinking. As he came in he leaned over and kissed her, and she turned to get away from him. When T.M. tried to turn on some lights, Searles stumbled into her, and they fell onto the floor in another room. Searles attempted to pull her nightgown up and tore a leg out of her underpants. T.M. began crying and begged him to quit. Searles momentarily stopped his struggle. T.M. told [577]*577him that his girlfriend was at home and to get out. The next thing T.M. knew, Searles was choking her. She passed out.
As a result of the incident, assault and attempted rape charges were filed. T.M. wanted only the assault charges to be filed, because she did not want to go through the humiliation of a jury trial in a small town where everybody knew her. At one point she asked the county attorney to dismiss the case, but he would not do so. The case was tried to a jury, and Searles was found not guilty.
c. Test for Admissibility of Other Crimes Evidence
In ruling on the admissibility of other crimes evidence under K.S.A. 60-455, the trial court must: (1) determine it is relevant to prove one of the facts specified in the statute; (2) determine the fact is a disputed, material fact; and (3) balance the probative value of the prior crime or civil wrong evidence against its tendency to prejudice the jury. State v. Nunn, 244 Kan. 207, 211, 768 P.2d 268 (1989); State v. Breazeale, 238 Kan. 714, 714 P.2d 1356 (1986).
(1.) Relevance
The trial court, at Searles’ trial, found that the evidence of the prior crimes was relevant to prove “identity” in the attempted rape charge. “Identity” is one of the facts specified in the statute.
In State v. Nunn, 244 Kan. 207, 212, 768 P.2d 268 (1989), this court noted:
“In State v. Bly, 215 Kan. 168, 523 P.2d 297 (1974), the leading case on the admissibility of evidence pursuant to K.S.A. 60-455, Justice Prager set forth eleven ■ basic principles to be considered. Principle number eleven reads:
“ 11. Where a similar offense is offered for the purpose of proving identity, the evidence should disclose sufficient facts and circumstances of the other offense to raise a reasonable inference that the defendant committed both of the offenses. In other words to show that the same person committed two offenses it is not sufficient simply to show that the offenses were violations of the same or a similar statute. There should be some evidence of the underlying facts showing the manner in which the other offense was committed so as to raise a reasonable inference that the same person committed both offenses. As pointed out by Mr. Justice Kaul in State v. Johnson, 210 Kan. 288, 502 P.2d 802:
“The quality of sameness is important when pondering the admission of other crimes to prove identity, (p. 294.)” ’ 215 Kan. at 177.”
[578]*578In Searles’ case, all of the crimes occurred in the early morning hours after Searles had been out drinking. The incident in Oklahoma occurred sometime after 3:30 a.m. The Montgomery County incident occurred at approximately 1:30 a.m. The attempted rape in the instant case occurred sometime after 12:30 a.m. but before 1:30 a.m., when Searles says he arrived home.
In each situation the victim was a divorced mother of a young child. P.A. had a three-year-old son living with her. T.M.’s daughter was living with her. The victim in the present case was a mother of three children, ages four years, two years, and three weeks. In each case, the victim knew Searles prior to the crime. In each case, the crime occurred in or very near the town where Searles was living.
At the time of the Oklahoma incident, Searles was married and his wife was expecting a child. At the time of the Montgomery County incident, Searles was living with his girlfriend. At the time of the attempted rape in the present case, he was married. His wife had a two-year-old at home and was expecting another child.
The crimes were perpetrated in a similar manner. In each case, Searles expected to have sexual intercourse with the victim, whom he knew. He had conversation with the victim before the rape or attempted rape occurred. In the Oklahoma case, Searles took off the victim’s underwear; he tore the victim’s underpants off of one leg in the Montgomery County case; and in the present case, the victim was found with her underpants torn from one leg and still hanging around the other leg.
Searles points to a number of dissimilarities in the prior cases and the present crime. He states the fact that the victims were single is almost inherent in the nature of the crime. Searles also notes that the majority of rapes occur between acquaintances.
The cases in which prior crimes have been used to prove identity have emphasized that the crimes need not be identical. It is sufficient if they were similar. State v. Williams, 234 Kan. 233, 670 P.2d 1348 (1983).
In the case at bar, the prior crimes are sufficiently similar to the present offense so as to raise a reasonable inference that [579]*579Searles committed all the offenses. The test of relevancy has been met.
(2.) Disputed Material Fact
“Identity” was an issue in the present case. The disputed material fact was whether or not the defendant was the one who committed the crime.
(3.) Probative Value Versus Prejudicial Effect
Before prior crimes evidence is admissible under K.S.A. 60-455, the trial court must also find that the probative value of the evidence — for the limited purpose for which it is offered — outweighs its prejudicial effect. As Breazeale pointed out, the evidence should not be admitted if the potential for natural bias and prejudice overbalances the contribution to the rational development of the case. 238 Kan. at 723. In the present case, it did not. The evidence of the prior crimes was not merely cumulative. The evidence of the prior crimes was an important and natural part of the whole trial.
Searles argues that he was unduly prejudiced by the admission of the prior crimes evidence because he had not been convicted of the prior crimes. However, in State v. Bly, 215 Kan. 168, 177, 523 P.2d 397 (1974), we stated in a summary of the basic principles of K.S.A. 60-455:
“To be admissible under 60-455 it is not necessary for the State to show that the defendant was actually convicted of the other offense. The statute specifically includes other crimes or civil wrongs. In fact an acquittal of the defendant of a prior offense does not bar evidence thereof where otherwise admissible. The acquittal bears only upon the weight to be given such evidence.”
A ruling on the admissibility of prior crimes evidence pursuant to K.S.A. 60-455 is within the discretion of the trial judge. That ruling will not be interfered with on review unless that discretion was abused, or unless the trial judge admitted evidence that clearly had no bearing on any of the issues. State v. Nunn, 244 Kan. at 211. In the present case that discretion was not abused,
d. Double Jeopardy — Collateral Estoppel
When the prosecutor seeks to admit evidence of a prior offense of which the defendant has been acquitted, the court must also determine whether the doctrine of collateral estoppel bars admission of the evidence.
[580]*580The United States Supreme Court in Ashe v. Swenson, 397 U.S. 436, 25 L. Ed. 2d 469, 90 S. Ct. 1189 (1970), defined collateral estoppel: “[W]hen an issue of ultimate fact has once been determined by a valid and final judgment, that issue cannot again be litigated between the same parties in any future law suit.” 397 U.S. at 443. The Court went on to explain that “the rule of collateral estoppel in criminal cases is not to be applied with the hypertechnical and archaic approach of a 19th century pleading book, but with realism and rationality.” 397 U.S. at 444.
Searles contends that, here, the trial court ignored the fact that the issue of “consent” in the previous cases was synonymous with the issue of “identity” because by acquitting Searles on the ultimate issue of consent, the jury in reality found that no crime had been committed. He argues the jury found that no violent, nonconsensual sexual offense had occurred. Thus, it could not be used to prove identity in the present case — a case involving a violent crime.
Searles’ argument is similar to the situation in State v. Irons, 230 Kan. 138, 630 P.2d 1116 (1981). The defendant in Irons steadfastly denied committing the crime. Thus, the issue of his identity was presented at trial. We found that the acquittal had to be based on the finding that he did not commit the prior offense. The issue of the defendant’s participation in the crime was settled, and collateral estoppel protected him against having to defend himself a second time. Irons, 230 Kan. at 144.
Recently the United States Supreme Court, in Dowling v. United States, 493 U.S. _, 107 L. Ed. 2d 708, 110 S. Ct. 668 (1990), revisited the issue of the admissibility of testimony from a prior trial in which the defendant was acquitted. Dowling, in our view, furnishes further support to the State’s position in the instant case.
Reuben Dowling had allegedly robbed a bank in the Virgin Islands while wearing a ski mask and carrying a small handgun. He was tried in the federal district court for various crimes, including bank robbery. The prosecution, relying on Fed. R. Evid. 404(b) (similar to K.S.A. 60-455), offered testimony by a woman who stated that (1) two men had entered her house two weeks after the bank robbery, one of them wearing a knitted mask, of a different color from that worn by the bank robber, [581]*581and carrying a small handgun; (2) she had unmasked this man after a struggle; and (3) defendant Dowling was the man she unmasked. The prosecution reasoned that this testimony was proper for the purposes of (1) strengthening the identification of Dowling as the bank robber by showing him wearing a mask and carrying a gun similar to those used by the robbery, and (2) linking Dowling to the other man involved in the intrusion at the woman’s home. The other man had also been spotted at the scene of the bank robbery in what the prosecution believed had been the intended getaway car.
Dowling contended that his prior acquittal of charges stemming from the house intrusion precluded the prosecution from introducing into evidence the woman’s testimony at trial in the bank robbery case. The Court commented:
“We disagree because, unlike the situation in Ashe v. Swenson, the prior acquittal did not determine an ultimate issue in the present case. This much Dowling concedes, and we decline to extend Ashe v. Swenson and the collateral estoppel component of the Double Jeopardy Clause to exclude in all circumstances, as Dowling would have it, relevant and probative evidence that is otherwise admissible under the Rules of Evidence simply because it relates to alleged criminal conduct for which a defendant has been acquitted.” 107 L. Ed. 2d at 717.
Searles’ defense in the Oklahoma case and in the Montgomery County case turned on the issue of consent. Searles, in his own brief, states, “However, in both of the other charges [the defendant] asserted that he did not sexually assault the women because the women consented to the sexual activity.” The issue in Searles’ two prior trials was consent. Searles admitted the sexual activity. Consent is not at issue in the present case. The issue that Searles now seeks to foreclose from consideration, identity, was not an issue in the prior cases.
The trial court followed the guidelines mandated by Ashe and Irons. Prior to trial, the trial court had available to it the transcripts from the prior cases. In allowing the evidence of the prior crimes, the court stated: [582]*582be given, and that’s what I’m going to do. So that’s my response for the record.”
[581]*581“He’s answered the issue of collateral estoppel. The issue in the other cases was consent. In this case it’s identity. He’s just covered all the bases. I can’t help but agree with him. Even though there may be some prejudicial effect, there always is. And that’s why it’s required that a limiting instruction
[582]*582The admission of prior crimes evidence, when a trial resulted in an acquittal, is a matter of discretion for the trial judge if the evidence is otherwise admissible and the collateral estoppel doctrine does not bar its introduction.
The collateral estoppel component of the double jeopardy clause was not violated. The K.S.A. 60-455 evidence was properly admitted.
e. The Scope of the Proffer
Prior to trial, at the hearing on the State’s motion to introduce K.S.A. 60-455 evidence, the trial court held that the evidence to be introduced at trial was restricted to what was proffered by the prosecutor at the hearing. The prosecutor proffered transcripts of the Oklahoma and Montgomery County cases. At trial, however, the prosecutor was allowed to elicit testimony regarding why one of the cases was not retried and why the witnesses in both cases did not want to testify. Searles contends that this evidence was not relevant to this case and merely served to unduly prejudice him.
Searles also contends that, because the testimony went beyond the proffer or the permissible use of evidence introduced pursuant to K.S.A. 60-455, his convictions must be set aside.
K.S.A. 60-401 defines relevant evidence as “evidence having any tendency in reason to prove any material fact.” The evidence here was relevant to refute Searles’ claim that the prior trial did not mean anything because the victim had not appeared for the second trial on the matter. Its use was proper. There was no error in allowing this testimony.
THE K.S.A. 60-455 LIMITING INSTRUCTION
Searles’ counsel objected to the trial court giving the PIK Crim. 2d 52.06 instruction, which stated: “Evidence has been admitted tending to prove that the defendant committed crimes other than the present crimes charged. This evidence may be considered solely for the purpose of proving the defendant’s identity.”
Defendant’s trial counsel objected to this instruction because Searles had been acquitted of one charge and the other was dismissed after the jury was unable to reach a verdict. Counsel [583]*583proposed that the trial court instruct the jury that Searles had been acquitted of one and the other was dismissed and that evidence of those cases could be considered solely for the purpose of attempting to prove identity. Counsel’s argument was that the language of PIK Crim. 2d 52.06 as applied to this case was wrong because it inferred, or at the very least left the impression, that Searles committed the other crimes and got away with them.
In State v. Macomber, 244 Kan. 396, 405, 769 P.2d 621 (1989), we stated:
“A trial court does not have the time to give the thought and do the research which has been put into the preparation of the Pattern Criminal Jury Instructions by the Advisory Committee on Criminal Jury Instructions to the Kansas Judicial Council. Therefore, where ‘pattern jury instructions are appropriate, a trial court should use them unless there is some compelling and articulable reason not to do so.’ ”
This is what the trial court did in this case. The instruction given follows PIK Crim. 2d 52.06 exactly.
The record shows it was made clear to the jury that Searles had been acquitted of one of the prior charges and the other charge was dismissed following a mistrial.
Although we view Searles’ requested instruction as a preferred statement covering the instant fact situation, the trial court did not commit error in giving PIK Crim. 2d 52.06.
BLOOD TEST TESTIMONY/GENETIC MARKINGS
Eileen Burnau, a criminalist with the KBI, performed tests to identify the genetic markings on blood found on Searles’ truck and on blood taken from Searles and from the victim’s parents. Specifically, Burnau tested the blood found on the bumper of the truck and compared it to the genetic markings of Searles and the parents. The blood on the bumper was determined to be EAP type B or EAP type CB, but, since the marker was not clear enough for positive identification, Burnau could not be certain which type it was. However, from her tests, Burnau concluded that, if the blood on the bumper was EAP type B blood, it would be consistent with the blood type Roxanne could have, and, if the blood on the bumper was EAP type CB, it could not have come from Roxanne. Burnau then testified that based upon population studies, only .48 percent of the overall population [584]*584would have the same blood characteristics as found in that particular scraping.
Dr. Edward Blake, a forensic serologist, also testified regarding tests he had performed on the blood found on the bumper of the truck. From his tests, Dr. Blake concluded the blood could have been, or was consistent with, Roxanne’s blood. Dr. Blake then combined the results of his tests with Burnau’s and concluded that .025 percent of the population, or one of 4,000 individuals, could have produced the bloodstain found on the bumper.
Defense counsel lodged a continuing objection to this evidence on the grounds the statistics were based on the assumption or the initial speculation that the blood was EAP type B, and not EAP type CB, which would have excluded the victim as the donor. The trial court noted the objection, but overruled it.
This court in State v. Washington, 229 Kan. 47, 622 P.2d 986 (1981), held that expert testimony of mathematical probabilities that a certain combination of events will occur simultaneously is generally inadmissible when based on estimations rather than on established facts. However, population percentages on the possession of certain combinations of blood characteristics, based upon established facts, are admissible as relevant to identification. 229 Kan. 47, Syl. ¶ 3.
Burnau explained the B/CB evaluation, and readily stated that she could only say it was a B or a CB type in the EAP system. Dr. Blake further explained the difficulty sometimes’ encountered in determining the B/CB type. Both experts pointed out that it is still a useful genetic marker system because, even if there is some ambiguity, it can be used to eliminate four other types.
This can be seen in the present case. In the EAP system, Searles is a type A. The scrapings from the bumper were either type B or CB in the EAP system. Thus, Searles was eliminated from being the donor of the blood on the bumper. At the same time, even though the blood on the bumper could only be said to be either an EAP type B or type CB, this finding did not eliminate Roxanne from being the donor of that blood.
Searles errs in assuming that “the statistics were based on the assumption or the initial speculation that the blood was EAP type [585]*585B,” or that “this typing [EAP type B] was the crucial fact upon which all other conclusions followed.” This is not accurate.
Burnau took into account in her figures that the blood could contain either EAP type B or EAP type CB. She also accounted for the statistic that only .48 percent of the population have blood characteristics that match those on the bumper by noting that the .48 percent includes people with EAP type B and those with EAP type CB blood.
The statistics, or the percent of the population that could have produced the bloodstain on the bumper, were based upon population studies for each of the genetic markers.
This method of calculating the percentage of the population, the so-called “product rule” of probability, which has, in combination, a number of genetic factors, has been specifically approved in State v. Stukey, 242 Kan. 204, 208, 747 P.2d 137 (1987).
Under State v. Washington, 229 Kan. at 59, challenges to the reliability of the testing affect the weight, not the admissibility, of the testimony. In this case also, the problem with the B/CB type affects the weight of the evidence and not its admissibility.
Neither of the experts stated that the blood on the bumper was the victim’s blood. What they said was that the blood on the bumper was consistent with blood that could have been Roxanne’s. There was no error in admitting the testimony of Eileen Burnau or of Dr. Blake.
Affirmed.