ORDER AND JUDGMENT *

This is a direct appeal by Maurice Mick-ling following his convictions on three counts: (1) possession of a firearm by a prohibited person in violation of 18 U.S.C. §§ 922 and 924; (2) possession of a controlled substance (namely, cocaine base) with intent to distribute in violation of 21 U.S.C. § 841; and (3) possession of a firearm in furtherance of a drug trafficking offense in violation of 18 U.S.C. § 924(c)(1)(A). He conceded guilt on Count 1. His only defense to Counts 2 and 3 was that he had possessed the cocaine base for personal use, not for distribution. He was found guilty by a jury on all three counts and sentenced to 192 months’ incarceration, although the advisory sentencing guideline range was much higher.

Mickling appeals his convictions on two grounds; both are subject to plain error review. First, he argues that the government’s expert witness, Detective Daniel Wiley, violated Federal Rule of Evidence 704(b), which prohibits an expert in a criminal case from opining on the defendant’s mental state when that mental state is an element of the crime charged. Second, Mickling argues that his due process rights were violated under Napue v. Illinois because the government knowingly offered perjured testimony, which was material, through its fact witness, Rhiannon Cheney.

Mickling seeks a reversal on all counts or, in the alternative, a reversal on Counts 2 and 3 and a remand on Count 1 for a new trial or resentencing. 1 We exercise jurisdiction pursuant to 28 U.S.C. § 1291 and affirm.

I

A, Factual Background

Law enforcement officers drove to a hotel in Denver to arrest Mickling on an outstanding warrant. Mickling walked out of the hotel and past an unmarked van in which a SWAT team was sitting. Recognizing him, one of the officers opened the door and ordered him to freeze. Mickling fled, removing a handgun from his waistband and throwing it across the street, and dropping a toiletries bag on the ground. He was apprehended, and the officers retrieved the bag and gun. The bag contained approximately 3.6 grams of cocaine base, a small digital scale, some plastic *823 wrapping, and various personal items. The gun was a nine-millimeter handgun loaded with fifteen rounds, with one round in the chamber. Mickling had approximately $750 in his pocket.

B. Trial

At trial, the government called Detective Wiley to testify as an expert witness about the drug trade in Denver. Wiley testified that he had reviewed the evidence in the case, and that the physical evidence included approximately 3.6 grams of crack cocaine, a small battery-powered scale, a nine-millimeter handgun, and approximately $750. He was then asked:

Q: Now, based upon everything that you have read about this case, and looked at in this case, based upon your experience and training, purchasing drugs, and working narcotic cases as an investigator, have you' formed an opinion as to whether or not the crack cocaine as in Government’s Exhibit 1 is consistent with possession with the intent to distribute or—

A: Yes—

Q: —or consistent with personal use?

A: It’s consistent with possession with intent to distribute.

Q: Now, why do you say that?

A: The fact that someone has 3.5 grams or an eightball of crack cocaine indicates that they are a dealer and not a user.

Q: What does — you testified the tools of the trade include guns, scales, money, plastic, what does this case have in it?

A: Guns, money, plastic, drugs, scale.

Q: And does that confirm your opinion?

A: It does. Yes. All of those factors together. Yes.

App. Ill at 256. Finally, he testified that hé had never seen a nondistributing user of crack cocaine who possessed 3.6 grams on their person.

The government also ealled a lay witness, Cheney, to testify about her personal relationship with Mickling. She testified that she knew Mickling, and had met him in 2010. She then said she did not see him again until 2013, and that in 2013, she saw him about seven or eight times. She said she never witnessed Mickling use crack cocaine, and had never known him to be a user of crack cocaine.

II

A, Standard of Review: Plain Error

Mickling raises two evidentiary challenges on appeal. He did not object when this evidence was presented at trial. Without a contemporaneous objection to alleged improper testimony, we review for plain error. United States v. Hill, 749 F.3d 1250, 1257 (10th Cir. 2014) (alleged improper opinion by an expert witness in a criminal case); United States v. Caballero, 277 F.3d 1235, 1243-44 (10th Cir. 2002) (alleged perjury constituting prosecutorial misconduct under Napue).

To satisfy the high threshold to achieve a reversal on plain error review, Mickling must show “[1] an ‘error’ [2] that is ‘plain’ and [3] that ‘affeet[s] substantial rights.’ ” United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993) (fourth alteration in original) (quoting Fed.R.Crim.P. 52(b)). If these three prongs are met, then we may exercise discretion to reverse only if we determine that “[4] the error ‘seriously affect[s] the fairness, integrity or public reputation of judicial proceedings.’” Id. (second alteration in original) (quoting United States v. Young, 470 U.S. 1, 15, 105 S.Ct. 1038, 84 L.Ed.2d 1 (1985)); see also United States v. Story, *824 635 F.3d 1241, 1244 (10th Cir. 2011) (citing United States v. Cotton, 535 U.S. 625, 631-32, 122 S.Ct. 1781, 152 L.Ed.2d 860 (2002)).

As regards the first and second prongs of plain error, an error is plain “if it is obvious or clear, i.e., if it is contrary to well-settled law.” Hill, 749 F.3d at 1258 (quoting United States v. Edgar, 348 F.3d 867, 871 (10th Cir. 2003)). Under the third prong of plain error, the error must affect the defendant’s substantial rights, prejudicing the defendant “by affect[ing] the outcome of the district court proceedings.” Olano, 507 U.S. at 734, 113 S.Ct. 1770. The burden is on the defendant to show this prejudice. Id. at 735, 113 S.Ct. 1770. “That is, he must demonstrate ‘a reasonable probability that but for the error claimed, the result of the proceeding would have been different.’ ” Hill, 749 F.3d at 1263 (quoting United States v. Trujillo-Terrazas, 405 F.3d 814, 818 (10th Cir. 2005)). This does not entail a preponderance standard, but rather requires “a probability sufficient to undermine confidence in the outcome.” Id. (quoting United States v. Hasan, 526 F.3d 653, 665 (10th Cir. 2008)). Even if the defendant can satisfy these three prongs, we may only exercise our discretion to reverse under the fourth prong if we are convinced that the error seriously affects the “fairness, integrity, or public reputation óf judicial proceedings.” Olano, 507 U.S. at 732, 113 S.Ct. 1770. In the present case, we need not reach the fourth prong under Olano because we resolve both issues presented under the third prong of plain error review.

B. First Alleged Error: Rule 704(b) Testimony

Federal Rule of Evidence 704(b) says, “In a criminal case, an expert witness must not state an opinion about whether the defendant did or did not have a mental state or condition that constitutes an element of the crime charged or of a defense. Those matters are for the trier of fact alone.” Fed.R.Evid. 704(b). We have interpreted Rule 704(b) to “only prevent[] experts from expressly stating the final conclusion or inference as to a defendant’s mental state. The rule does not prevent the expert from testifying to facts or opinions from which the jury could conclude or infer the defendant had the requisite mental state.” United States v. Goodman, 633 F.3d 963, 970 (10th Cir. 2011) (quoting United States v. Richard, 969 F.2d 849, 854-55 (10th Cir. 1992)).

For the purposes of our ruling on the Rule 704(b) issue, we will assume error was committed and that it was plain. To determine whether this alleged error prejudiced Mickling by affecting the outcome of his trial, we look to whether he has shown “a reasonable probability that but for the error claimed, the result of the proceeding would have been different,” which is “sufficient to undermine confidence in the outcome.” Hill, 749 F.3d at 1263 (first quoting Trujillo-Terrazas, 405 F.3d at 818; then Hasan, 526 F.3d. at 665). In cases involving Rule 704(b) on plain error review, we have affirmed on the basis that there was sufficient evidence to support a conviction even without the improper testimony. See, e.g., United States v. Archuleta, 737 F.3d 1287, 1298-99 (10th Cir. 2013) (“Even if Lujan’s testimony violated Rule 704(b), however, Archuleta cannot demonstrate plain error.... [TJhree of his coconspirators testified that Archuleta not only participated in the smuggling scheme but also orchestrated it.... Thus, even in the absence of the challenged response by Lujan to the hypothetical question, there was more than sufficient evidence presented to establish [the elements of the crime].”); United States v. Garza, 566 F.3d 1194, 1202 (10th Cir. 2009) *825 (“[T]here was solid admissible evidence of Mr. Garza’s intent.”). This conforms with the plain error standard. If we conclude upon review of all of the evidence presented that there is no reasonable probability that but for the admission of the challenged testimony the outcome of the trial would have been different, we must affirm.

Here, the items that Mickling had on his person constituted more than sufficient evidence from which a jury could conclude that he possessed cocaine base with an intent to distribute and that he possessed a firearm in furtherance of that distribution. He admitted that he possessed the loaded nine-millimeter handgun, and he possessed several items that to the jury would likely signal an intent to distribute, even without Wiley’s testimony. And Wiley testified to several facts and opinions from which the jury may have found guilt even without his testimony referring to intent. This evidence, when coupled with the evidence retrieved at the scene, causes us to conclude that Mickling has not demonstrated a reasonable probability that but for the challenged testimony he would not have been convicted on Counts 2 and 8.

C. Second Alleged Error: Napue Claim

The Supreme Court in Napue v. Illinois articulated that the defendant’s, rights to due process under the Fourteenth Amendment are violated when he is convicted “through use of false evidence, known to be such by representatives of the State” or “when the State, although not soliciting false evidence, allows it to go uncorrected when it appears.” Napue, 360 U.S. 264, 269, 79 S.Ct. 1173 (1959); see Caballero, 277 F.3d at 1243. To establish this Napue violation, the defendant must show that the testimony was false, the prosecution knew the testimony was false, and the testimony was material. Caballero, 277 F.3d at 1243. Ordinarily, under Napue, “[t]he false testimony is material ‘unless failure to disclose [the perjury] would be harmless beyond a reasonable doubt.’” United States v. Garcia, 793 F.3d 1194, 1207 (10th Cir. 2015) (second alteration in original) (quoting United States v. Bagley, 473 U.S. 667, 680, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985)), cert. denied, 577 U.S. -, 136 S.Ct. 860, 193 L.Ed.2d 758 (2016). Because plain error review applies in this case, the burden is on Mickling under the third prong to show that the alleged' violation likely affected the outcome of the trial.

Mickling argues that Cheney committed perjury when she testified that she first met him in 2010. He argues that this testimony was false because he was incarcerated for the entirety of 2010. He also alleges that the government was aware that Mickling pled guilty to various felonies in late 2009 and was incarcerated for all of 2010. And he argues this was material because the government characterized Ms. Cheney’s testimony as “ ‘very important’ to the central issue in the case— whether Mickling possessed the cocaine base in order to use it or distribute it to others.” Aplt. Br. at 20 (quoting App.. Ill at 370 (government’s rebuttal closing argument)).

Even if we assume the elements of a Napue violation were satisfied here, Mickling has not met his burden under the third prong of plain error review. He has not shown that the outcome of the trial would likely have been different had Cheney testified to first meeting Mickling in a different year. Mickling primarily argues that Cheney’s testimony was very important to the government’s casé, by its own admission. However, we are not convinced that the specific fact that Cheney met Mickling in 2010 was integral to the government’s case. Cheney testified that *826 she met Mickling in 2010 and that she did not see him use crack cocaine at that time. However, the main focus of the government’s questioning was on the subsequent time she spent with Mickling in 2013— during which she also testified she had not seen him use crack cocaine. She said she had seen him seven or eight times in 2013, but- was “not exactly sure” how many times she saw him in 2010. And where Mickling argues that the government, in its rebuttal closing argument, told the jury that Cheney’s testimony was important, the government in fact referred only to the “seven or eight times” Cheney was with Mickling — that is, in 2013 — not the initial time they met.

Consider what would have happened if the government had disclosed the perjury. If Cheney was mistaken about the year, and in fact met Mickling in 2009 (for example), then it is extremely unlikely that there would be any change in the jury’s verdict if the government disclosed Cheney’s error. The same is true if Cheney did not actually meet Mickling until 2013. The jury would still have Cheney’s testimony that she was with Mickling seven or eight times in 2013 and that she had not seen him use crack cocaine during any of those occasions. Both sides focused their examination on the time period in 2013, because the events leading to Mickling’s arrest had occurred in 2013 — any drug activity or lack thereof that occurred in 2010 would be almost entirely irrelevant to whether Mickling was a drug user or distributor in late 2013. Further, because Cheney did not even remember what time of year in 2010 she met Mickling, the jury very likely did not focus on this part of her testimony. Even if Mickling established a Napue violation, - he has not satisfied the more stringent plain error standard that requires a strong showing of prejudice.

Ill

The judgment of the district court is AFFIRMED.