ORDER
The Opinion filed May 5, 2008 and published at 525 F.3d 787 (9th Cir.2008) is hereby AMENDED as follows: Page 790, Footnote 1: Remove “Though counsel for Respondents sought to distance himself from this concession at oral argument before us, Respondents are judicially es-topped from disavowing their prior representations to the courts. See Helfand v. Gerson, 105 F.3d 530, 534-36 (9th Cir.1997); Russell v. Rolfs, 893 F.2d 1033, 1037-39 (9th Cir.1990).”
The petition for rehearing and suggestion for rehearing en banc are still pending.
WARDLAW, Circuit Judge:
At Petitioner Troy Brown’s trial for sexual assault, the Warden and State’s (“Respondents”) deoxyribonucleic acid (“DNA”) expert provided critical testimony that was later proved to be inaccurate and misleading. Respondents have conceded at least twice that, absent this faulty DNA testimo[790] ny, there was not sufficient evidence to sustain Troy’s conviction.1 In light of these extraordinary circumstances, we agree with District Judge Philip M. Pro’s conclusions that Troy was denied due process, and we affirm the district court’s grant of Troy’s petition for writ of habeas corpus.
I. FACTUAL AND PROCEDURAL BACKGROUND2
A. The Crime
In the early morning of January 29, 1994, Jane Doe,3 a nine-year-old girl, was sexually assaulted in the bedroom of her trailer home in Carlin, Nevada. At the time, Jane was home alone with her four-year-old sister while their mother, Pam, was drinking at a bar and their step-father, Wayne Henle, was working the night shift. Troy was arrested, tried, and convicted for this crime.
Earlier that night, Pam received a phone call from Raquel Brown, who is married to Troy’s brother, Trent, inviting Pam to join her and Trent for a drink at the local bar, CG’s, and asking if Jane could babysit Raquel’s children while they were at the bar. At 6:30 p.m., Pam took Jane and her sister to Raquel’s house, which is located across the street; Pam and Raquel left to meet Trent at CG’s. Raquel and Trent left CG’s at 7:30 p.m., and Pam remained at the bar. Raquel and Trent returned home and found Jane and her sister watching a movie. When the movie concluded at 9:30 p.m., Raquel took the children home. Jane, wanting to let Pam know they arrived home safely, first called CG’s, where the line was busy. Jane then called Peacock Bar, where Troy answered the phone and stated that Pam was at CG’s but that he would deliver the message. By the time Troy arrived at CG’s, Pam was on the phone with Jane.
When the conversation ended, Pam accompanied Troy to Peacock Bar where they had a drink. Troy was clearly drunk, but “he behaved like a gentleman and made no sexual advances toward” Pam. Pam stated that the last time she saw Troy was between 11 p.m. and midnight. However, one bartender stated that Troy left the bar no later than 12:20 a.m., and another bartender stated that she believed she saw Troy at the bar at 1:30 a.m. Between midnight and 12:30 a.m.,4 Jane called Pam at the bar and explained that some man was at the trailer looking for Pam and had hurt her. When Pam arrived home, she found Jane covered in blood from the waist down and called 911. A police officer and the paramedics responded. Jane stated to the paramedic that she felt pain in her vaginal area, and Pam responded that her ex-husband had done this because he threatened to “f— [Pam’s] daughter in order to get back at [Pam].”
Later at the hospital, vaginal and anal penetration were confirmed. Jane had bruises on her neck and scratches on her face. A vaginal smear was taken because sperm was present. Debris was collected [791] from her teeth because she stated she had bitten the assailant’s hands.
Jane described the assailant to the police that night as follows:
[H]e did not wear a hat and had blonde or sandy-colored hair which was curly at the bottom and thinning on top; she thought he had a small moustache; he was wearing dark jeans, a black jacket with “a zipper for sure,” a western type shirt, boots, and a watch which scraped her face____[She] stated that the assailant smelled like cologne but that it was an “awful smell” ... [like] “beer or puke or something.”
That night, Troy was wearing a cowboy hat, dark jeans, a black satin jacket with an orange and yellow CG’s logo on the back, and boots. Two witnesses testified that, at 1:05 a.m. that morning, they saw near Jane’s trailer a man wearing a cowboy hat, dark jeans, and a black satin jacket with a bright green emblem on the back that looked like a skull or bandit.
Troy stated that he had been drinking steadily that night and, while walking home to his trailer located ten trailers away from Jane’s, had vomited several times, soiling his pants and shirt. When he arrived home, Troy’s brother, Travis, awoke from sleeping on the couch. Travis stated that it was 1:32 a.m. when he awoke and that he did not see any traces of blood in the house. Troy washed his clothes as soon as he returned home because he was leaving that day to go to Utah for a week and all of his clothes were already packed. When a police officer arrived at 5 a.m. to question Troy, he saw no blood on Troy or his boots; he also checked Troy’s hands, which did not have any evidence of bite marks.
Jane also stated that she fell asleep with a night light on, but that the.man who assaulted her must have turned it off because it was off when the man left. Troy’s fingerprints were not found anywhere in Jane’s trailer, and the one fingerprint found on the night light did not match Troy’s.
When the police pressed Jane to tell them who the assailant reminded her of, Jane stated “Troy,” and when the police responded “Who?,” Jane stated “Trent. Yes, Trent.” Jane explained that Trent was Raquel’s husband. Jane also stated that the assailant’s hair looked like Troy’s but then changed her mind and said it looked like Trent’s hair. A number of days after the assault, Jane witnessed a television report of Troy’s arrest and stated that “she knew that the man on televi-sión was her assailant.” Jane also told the police officers that the man she had seen on television had sent her flowers. The card that came with the flowers was signed by Raquel and Trent, not Troy. When the police showed Jane pictures that included Troy’s picture and other people that she did not know, Jane was unable to identify Troy as her attacker.
After Troy left for Utah, he contacted the Carlin police to inquire whether he was wanted for arrest, but he was told that he was not. Knowing that he was under suspicion, Troy requested a full-body examination to be conducted by a nurse in order to record his physical condition. On or about .February 7, 1994, Troy voluntarily surrendered to the police and was arrested. During the interrogation and throughout all proceedings, Troy has repeatedly denied involvement in the crime.
B. State Court Proceedings
At trial, Respondents presented the testimony of DNA expert Renee Romero of the Washoe County Sheriffs Office Crime Lab. Romero testified that, among other things, there was a 99.99967 percent chance that Troy was the assailant.
[792] The jury found Troy guilty of two counts of sexual assault on a child under the age of fourteen, in violation of Nevada Revised Statutes 200.366, and one count of abuse or neglect of a child resulting in substantial bodily harm, in violation of Nevada Revised Statutes sections 200.508, 432B.020, and 432B.070. Troy appealed to the Nevada Supreme Court, claiming, inter alia, the district court abused its discretion when sentencing him, the bar against double jeopardy was violated by the duplica-tive convictions for sexual assault and abuse or neglect of a child, the DNA evidence was improperly admitted, and the evidence was insufficient to sustain his conviction. The Nevada Supreme Court vacated the third charge and remanded for resentencing on the second sexual assault count. The trial court resentenced Troy to life with the possibility of parole after ten years on both sexual assault counts, to run consecutively. Troy again appealed to the Nevada Supreme Court, which rejected his appeal. Troy next filed a state petition for post-conviction relief, and, after holding an evidentiary hearing, the state courts denied relief.
C. Federal Court Proceedings
On February 6, 2004, Troy filed his federal petition for writ of habeas corpus pursuant to 28 U.S.C. § 2254, arguing, inter alia, violations of due process and ineffective assistance of counsel. Judge Pro permitted Troy to expand the record, admitting, among other things, an uncontested report discrediting Romero’s testimony by Dr. Laurence Mueller (the “Mueller Report”), a professor of Ecology and Evolutionary Biology at the University of California, Irvine.
The district court granted Troy’s petition. First, the district court concluded that, in light of the Mueller Report, Romero’s testimony was unreliable. Absent that testimony, no rational trier of fact could conclude beyond a reasonable doubt that Troy was guilty of each and every element of the offenses with which he was charged. The district court also concluded that Troy’s attorney’s failure to diligently defend against Respondents’ DNA testimony, as well as his failure to investigate the alibi of Henle, a potential suspect, amounted to ineffective assistance of counsel. Respondents timely appealed.
II. STANDARD OF REVIEW
Because Troy filed his petition after April 24, 1996, it is governed by the Antiterrorism and Effective Death Penalty Act, 28 U.S.C. § 2254(d). Section (d)(1) of that provision provides:
An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim—
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.
A decision is “contrary to ... clearly established” Supreme Court precedent “if the state court applies a rule that contradicts the governing law set forth in [the Supreme Court’s] cases or if the state court confronts a set of facts that are materially indistinguishable from a decision of [the Supreme Court] and nevertheless arrives at a result different from [the Supreme Court’s] precedent.” Lockyer v. Andrade, 538 U.S. 63, 73, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003) (internal quotation marks omitted). A decision is an “unreasonable application of ... clearly established” Supreme Court precedent “if the state court identifies the correct governing [793] legal principle from [the Supreme Court’s] decisions but unreasonably applies that principle to the facts of the prisoner’s case.” Id. at 75, 123 S.Ct. 1166 (internal quotation marks omitted). Under the latter inquiry, “[t]he state court’s application of clearly established law must be objectively unreasonable.” Id.
We review a district court’s decision to grant or deny a habeas petition under 28 U.S.C. § 2254 de novo. Bean v. Calderon, 163 F.3d 1073, 1077 (9th Cir.1998).
III. DISCUSSION
Troy asserts that there was insufficient evidence to convict him. His argument rests on the admission of Romero’s later discredited testimony regarding the DNA evidence, which was introduced without rebuttal at trial. Respondents have conceded that absent introduction of Romero’s DNA evidence, the remaining evidence is insufficient to sustain Troy’s conviction. Having reviewed the record ourselves, we affirm the district court’s conclusion that, had Romero’s inaccurate and unreliable testimony on the DNA evidence been excluded, there would have been insufficient evidence to convict Troy on each essential element of the offenses beyond a reasonable doubt. We further agree with the district court’s conclusion that the Nevada Supreme Court’s decision was both “contrary to” and an “unreasonable application of’ established United States Supreme Court precedent.
A. Exhaustion
Respondents erroneously contend that Troy failed to exhaust his insufficiency claim in the Nevada courts. Troy in fact raised this claim on direct appeal, and the Nevada Supreme Court concluded that the totality of the evidence-considering both the DNA and non-DNA evidence together-was sufficient to uphold the conviction. Brown v. State, 113 Nev. 275, 934 P.2d 235, 240-42 (Nev.1997); see also O’Sullivan v. Boerckel, 526 U.S. 838, 845, 119 S.Ct. 1728, 144 L.Ed.2d 1 (1999) (“[S]tate prisoners must give the state courts one full opportunity to resolve any constitutional issues by invoking one complete round of the State’s established appellate review process.”).
B. Motion to Supplement the Record
Respondents argue that the district court erred by granting Troy’s request to supplement the record with the Mueller Report. Whether we apply the de novo or abuse of discretion standard of review to a district court’s expansion of the record in support of a claim of insufficient evidence is an open question. See Cooper-Smith v. Palmateer, 397 F.3d 1236, 1241 n. 12 (9th Cir.2005). However, applying either standard of review, the district court’s decision to expand the record here was legally proper.
Under 28 U.S.C. § 2254(e)(2), a claimant who “failed to develop the factual basis of a claim in State court proceedings” will not be permitted to supplement the record in federal court unless the claim relies on (1) “a new rule of constitutional law,” made retroactive to cases on collateral review by the Supreme Court, that was previously unavailable; or “a factual predicate that could not have been previously discovered through the exercise of due diligence”; and (2) “the facts underlying the claim would be sufficient to establish by clear and convincing evidence that but for constitutional error, no reasonable factfinder would have found the applicant guilty of the underlying offense.” Although none of these conditions is met here, “[a]n exception to this general rule exists if a Petitioner exercised diligence in his efforts to develop the factual basis of his claims in state [794] court proceedings.” Cooper-Smith, 397 F.3d at 1241.
The district court correctly found that Troy “presented a comprehensive discussion of the DNA evidence” before the Nevada Supreme Court. This finding is supported by numerous challenges to the DNA evidence raised in Troy’s state court briefs. Troy’s attempts were “reasonable” and therefore “diligent.” See Williams v. Taylor, 529 U.S. 420, 435, 120 S.Ct. 1479, 146 L.Ed.2d 435 (2000) (“Diligence for purposes of [§ 2254(e)(2) ] depends upon whether the prisoner made a reasonable attempt, in light of the information available at the time, to investigate and pursue claims in state court.”). Moreover, as the district court found, the Mueller Report merely clarifies, rather than fundamentally alters, the DNA evidence and expert testimony that was already before the Nevada courts. See Vasquez v. Hillery, 474 U.S. 254, 260, 106 S.Ct. 617, 88 L.Ed.2d 598 (1986) (“We hold merely that the supplemental evidence presented by respondent did not fundamentally alter the legal claim already considered by the state courts, and, therefore, did not require that respondent be remitted to state court for consideration of that evidence.”). Therefore, the district court did not err by admitting the Mueller Report.
C. Merits
We agree with the district court that the Nevada Supreme Court’s decision was both “contrary to” and “an unreasonable application of’ Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979). In Jackson, the Supreme Court held that a conviction must be upheld if, “after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Id. at 319, 99 S.Ct. 2781. “[T]he standard must be applied with explicit reference to the substantive elements of the criminal offense as defined by state law.” Id. at 324 n. 16, 99 S.Ct. 2781; see also Chein v. Shumsky, 373 F.3d 978, 983 (9th Cir.2004) (en banc).
1. “Contrary to”
When addressing Troy’s insufficiency claim, the Nevada Supreme Court stated that “[t]he standard of review for sufficiency of the evidence upon appeal is whether the jury, acting reasonably, could have been convinced of the defendant’s guilt beyond a reasonable doubt.” Brown, 934 P.2d at 241 (citing Kazalyn v. State, 108 Nev. 67, 825 P.2d 578 (Nev.1992)). It then compiled — in one paragraph — the facts that supported its conclusion. Id. at 241-42.
We agree with the district court that the Nevada Supreme Court’s decision was “contrary to” Jackson, as the Nevada Supreme Court did not apply the Jackson standard. Though the Nevada Supreme Court in previous cases had applied the Jackson standard, see, e.g., Wilson v. State, 99 Nev. 362, 664 P.2d 328, 336 (Nev. 1983), here, the state court applied the standard set forth in Kazalyn v. State. Brown, 934 P.2d at 241. As the district court pointed out, “[t]he Kazalyn standard only requires a reasonable jury — not a rational one.” Moreover, under Kazalyn, a reviewing court assesses whether the jury could have been “convinced of the defendant’s guilt”; the Jackson standard is different, requiring the reviewing court to assess “the essential elements of the crime.” The Nevada Supreme Court failed to analyze each of the essential elements of the substantive state crime. Instead, it merely recited all of the facts cumulatively without analyzing whether each or any of those facts established an essential element of the counts of convie[795] tion beyond a reasonable doubt, and that a rational juror could have so found. See Chein, 373 F.3d at 983-93 (analyzing materiality and falsity of statements made in three separate perjury counts to hold that no rational juror could have found the defendant guilty of each element of perjury beyond a reasonable doubt). Therefore, the Nevada Supreme Court’s decision was contrary to Jackson. In fact, as demonstrated, infra, once the unreliable DNA testimony is excluded, a proper application of the Jackson standard leads to the conclusion that not all of the essential elements of the crime were in fact proven beyond a reasonable doubt.
2. “Unreasonable application of”
The district court also correctly concluded that the Nevada Supreme Court’s decision was “an unreasonable application of’ Jackson because, in light of the Mueller Report, no rational trier of fact could have found Troy guilty beyond a reasonable doubt on the evidence presented at trial. The validity and accuracy of the Mueller Report went unchallenged by Respondents, and the district court found it to be credible. We review this finding for clear error, and conclude the district court did not clearly err. See Buckley v. Terhune, 441 F.3d 688, 694 (9th Cir.2006) (en banc).
The Mueller Report indicates that Romero’s testimony was unreliable for two main reasons. First, Romero testified that there was a 99.99967 percent chance that Troy’s DNA was the same as the DNA discovered in Jane’s underwear-or, in other words, that the science demonstrated a near 100 percent chance of Troy’s guilt. This assertion was incorrect, as it falls directly into what has become known as the “prosecutor’s fallacy.” The prosecutor’s fallacy occurs when the prosecutor elicits testimony that confuses source probability with random match probability. Put another way, a prosecutor errs when he “presents statistical evidence to suggest that the [DNA] evidence indicates the likelihood of the defendant’s guilt rather than the odds of the evidence having been found in a randomly selected sample.” United States v. Shonubi, 895 F.Supp. 460, 516 (E.D.N.Y.1995) (internal quotation marks and citation omitted), vacated on other grounds, 103 F.3d 1085 (2d Cir.1997); see also United States v. Chischilly, 30 F.3d 1144, 1157 (9th Cir.1994) (“To illustrate, suppose the ... evidence establishes that there is a one in 10,000 chance of a random match. The jury might equate this likelihood with source probability by believing that there is a one in 10,000 chance that the evidentiary sample did not come from the defendant. This equation of random match probability with source probability is known as the prosecutor’s fallacy.”); Richard Lempert, Some Caveats Concerning DNA as Criminal Identification Evidence, 13 Cardozo L. Rev. 303, 305-06 (1991). Such a fallacy is dangerous, as the probability of finding a random match can be much higher than the probability of matching one individual, given the weight of the non-DNA evidence. See William C. Thompson and Edward L. Schumann, Interpretation of Statistical Evidence in Criminal Trials, 11 L. And Hum. Behav. 167, 170-71 (1987) (noting that the prosecutor’s fallacy “could lead to serious error, particularly where the other evidence in the case is weak and therefore the prior probability of guilt is low”).
Here, Romero initially testified that Troy’s DNA matched the DNA found in Jane’s underwear, and that 1 in 3,000,000 people randomly selected from the population would also match the DNA found in Jane’s underwear (random match probability). After the prosecutor pressed her to put this another way, Romero testified that there was a 99.99967 percent chance [796] that the DNA found in Jane’s underwear was from Troy’s blood (source probability). This testimony was misleading, as it improperly conflated random match probability with source probability. In fact, the former testimony (1 in 3,000,000) is the probability of a match between an innocent person selected randomly from the population; this is not the same as the probability that Troy’s DNA was the same as the DNA found in Jane’s underwear, which would prove his guilt. Statistically, the probability of guilt given a DNA match is based on a complicated formula known as Bayes’s Theorem, see id. at 170-71 n. 2, and the 1 in 3,000,000 probability described by Romero is but one of the factors in this formula. Significantly, another factor is the strength of the non-DNA evidence. Here, Romero improperly conflated random match and source probability, an error that is especially profound given the weakness of the remaining evidence against Troy. In sum, Romero’s testimony that Troy was 99.99967 percent likely to be guilty was based on her scientifically flawed DNA analysis, which means that Troy was most probably convicted based on the jury’s consideration of false, but highly persuasive, evidence.
Second, Romero inaccurately minimized the likelihood that Troy’s DNA would match one of his four brothers’ DNA, thus underestimating the likelihood that one of Troy’s brothers could have been the perpetrator. She testified that there was a 25 percent chance of two brothers sharing both alleles at one locus, and, using that figure, a 1/6500 chance that one of Troy’s brothers would match Troy’s DNA at all five loci.5 The Mueller Report indicated that Romero’s calculation was incorrect, as the correct figure is 1/1024. More importantly, Romero’s testimony is misleading because it presented the narrowest interpretation of the DNA evidence. Had Romero accounted for Troy’s four brothers, two of whom lived in Carlin and two of whom lived in neighboring Utah, the chance that Troy’s DNA would match at least one of his four brothers’ DNA can increase to 1/66 — almost one hundred times the probability asserted by Romero. This omission was especially egregious given that the victim, Jane, had twice identified Troy’s brother, Trent, as the assailant. Again, Respondents introduced nothing to contradict the findings of the Mueller Report.
A federal court on habeas may exclude evidence admitted in the state court if the evidence “rendered[the] trial so fundamentally unfair as to violate federal due process.” Butcher v. Marquez, 758 F.2d 373, 378 (9th Cir.1985). We agree with the district court that Romero’s testimony was [797] unreliable, as it was inaccurate and ignored logical implications about Troy’s four brothers, each of whom lived in the general vicinity. Admission of this unreliable testimony most certainly rendered the trial fundamentally unfair, as even Respondents concede that “[t]here was insufficient evidence to convict the Defendant unless the DNA evidence established his guilt.” Thus, the admission of Romero’s unreliable and misleading testimony violated Troy’s due process rights, and the district court did not err in excluding it. See United States v. Scheffer, 523 U.S. 303, 309, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998) (“State and Federal Governments unquestionably have a legitimate interest in ensuring that reliable evidence is presented to the trier of fact in a criminal trial. Indeed, the exclusion of unreliable evidence is a principal objective of many evi-dentiary rules.”).
After excluding Romero’s testimony, the district court weighed the sufficiency of the remaining evidence in the light most favorable to the prosecution, Jackson, 443 U.S. at 319, 99 S.Ct. 2781, and concluded that “there [is] sufficient conflicting testimony to raise a reasonable doubt in the mind of any rational trier of fact.” On appeal, Respondents argue that there is much evidence to support the conviction. However, it is Respondents’ burden to establish guilt beyond a reasonable doubt for each and every element of the offense, a burden that Respondents have not carried here.
The district court thoroughly catalogued the numerous inconsistencies that would raise a reasonable doubt as to Troy’s guilt in the mind of any rational juror. Three witnesses disagreed about the time at which Troy left CG’s to return home. Notably, one witness testified that Troy remained at the bar at 1:30 a.m., thirty to ninety minutes after the assault occurred. Moreover, although Jane at times identified Troy as her attacker, twice she identified Trent as the assailant. There is also considerable conflict between Jane’s description of her attacker and Troy’s clothing and appearance that night. For example, Troy’s jacket was zipperless, but Jane testified that her assailant’s jacket had “a zipper for sure.”
The prosecution’s theory is also undermined by the testimony of Troy’s brother and roommate, Travis, who testified that he did not see blood on Troy’s boots or notice anything unusual about Troy when he arrived home at 1:32 a.m. Furthermore, early the next morning, when an officer examined Troy, he found no evidence of marks on Troy’s hands or blood on Troy’s clothing, which would have been consistent with Troy being the attacker. That Troy laundered his clothing, though plausibly consistent with him being the assailant, is also consistent with his testimony that he vomited on himself on the walk home, and that he wanted to clean his clothes before his trip to Utah the following day.
The manner in which the forensic evidence at the scene was collected and examined raises doubt as well. Troy’s fingerprints did not match the fingerprint on the night light in Jane’s room, which Jane testified her attacker turned off before waking her up. Moreover, neither Jane’s bedding nor the pubic hairs discovered in a jacket in Jane’s bedroom were tested for DNA samples.
At all times, Troy has denied involvement in the crime. He also took actions inconsistent with having something to hide. While in Utah, he called the Carlin police to inquire whether he was wanted for arrest. Knowing that he was under suspicion, he voluntarily submitted to a full-body examination to record that he had no markings consistent with Jane’s description of the attack.
[798] The conflicts in the evidence are simply too stark for any rational trier of fact to believe that Troy was the assailant beyond a reasonable doubt, an essential element of any sexual assault charge. This conclusion is confirmed by Respondents’ own concessions. Therefore, the Nevada Supreme Court’s decision was “an unreasonable application of’ Jackson.
IV. CONCLUSION
Because we affirm the district court’s grant of Troy Brown’s habeas petition on due process grounds, we need not reach his arguments regarding ineffective assistance of counsel. The district court’s grant of Troy’s petition for writ of habeas corpus and reversal of his conviction is AFFIRMED. Respondents shall retry Troy within 180 days or shall release him from custody.
AFFIRMED.