PER CURIAM:

Defendant-appellant, Khachatour C. So-gomonian (“Sogomonian”), appeals from a June 6, 2000 judgment entered in the United States District Court for the Western District of New York (John T. Elfvin, Judge). The three-count indictment against Sogomonian charged him with two counts (Counts 1 and 2) of violating 18 U.S.C. § 922(g)(1) and 18 U.S.C. § 924(a)(2) and one count (Count 3) of violating 18 U.S.C. § 922(k) and 18 U.S.C. § 924(a)(1)(B). 1 Sogomonian’s defense at trial was that he did not knowingly possess either of the firearms in question. Judgment in this case was entered after Sogo-monian was found guilty on Count 1 of the indictment. The jury was unable to reach a verdict on Counts 2 and 3 of the indictment, and therefore Counts 2 and 3 were *350 dismissed. Judge Elfvin sentenced Sogo-monian to fifteen months’ imprisonment, to be followed by a period of two years’ supervised release, and a $100 special assessment. On appeal, Sogomonian raises three issues, which all focus on Judge Elf-vin’s interaction with the jury.

I. BACKGROUND

On March 11, 1997, Sogomonian and two of his cousins, who do not speak English, traveled across the country from California to Boston in a rented van. They made many stops to sell antique rugs on the trip. On the return trip, the cousins drove through Western New York and for a very short time into Canada.

On March 22, 1997, a little after 3 a.m., Sogomonian drove the rented van back into the United States from Canada at the Rainbow Bridge, Niagara Falls, New York. Apparently, Sogomonian had been sleeping when his cousins drove into Canada and thus was unaware that he had been in Canada. Therefore, when asked by the customs inspector how long he had been in Canada, Sogomonian responded that he and his cousins had not been in Canada. As a result of this answer, Sogomonian and his cousins were directed to proceed from the primary inspection area to the secondary inspection area.

When questioned about the presence of firearms in the van, Sogomonian answered that there was a 9 millimeter pistol in the side compartment toward the rear of the van. Sogomonian also told the Customs Inspectors that the gun was not loaded, that there were two magazines somewhere in the van, and that the 9 millimeter pistol was registered in his father’s name. Customs Inspectors Ballentine and Langan proceeded to search the van, and Ballen-tine found the 9 millimeter pistol. The magazines for the 9 millimeter pistol were also found in the van. Langan also found a .25 caliber pistol with its serial number obliterated between the seat and the seat back of the rear seat of the van. When asked if there were other firearms in the van besides the 9 millimeter pistol and to whom they might belong, Sogomonian responded that there might be a .22 or .25 caliber pistol in the van and that “basically, it belongs to me.”

Sogomonian was arrested for violating 18 U.S.C. § 922(k), which makes it illegal to possess a firearm with its serial number removed or obliterated. Later in the morning of March 22, 1997, while awaiting his initial appearance, Sogomonian was in the custody of Special Agent Vadala of the United States Customs Service. Vadala testified that Sogomonian told him that the guns in the van were for protection, that his friends in California told him to take the guns for protection, and that it was stupid and a big mistake for him to have the guns. Vadala also testified that Sogo-monian inquired as to whether there was any way to get out of the situation that he was in. Sogomonian denied making any statements suggesting that he knew the guns were in the van. Sogomonian also pointed out that Agent Vadala made three reports of the alleged admissions, each with different details. These reports contained changes concerning the location where Sogomonian’s statements were made and to whom the statements were made.

Subsequent investigation revealed that Sogomonian had been convicted of the Illegal Possession of a Narcotic Controlled Substance, as a felony, in violation of Section 11350 of the California Health and Safety Code. This crime was punishable by imprisonment for a term exceeding one 'year. Therefore, Sogomonian was charged with two counts of violating 18 U.S.C. § 922(g)(1), which makes it illegal for an individual who has previously been convict *351 ed of a crime punishable by imprisonment for a term exceeding one year to possess a firearm.

Sogomonian’s defense at trial was that he did not knowingly possess either of the firearms in question. Sogomonian’s father bolstered his son’s defense by testifying that he had hid the 9 millimeter pistol and the magazines inside the rugs in late April 1996. Sogomonian testified that he had trouble renting a van for the trip across the country, and when he finally secured a rental van, it was not cleaned before the trip began. Also testifying at trial was a fingerprint specialist with the Bureau of ATF who testified that no identifiable fingerprints were found on either of the firearms or the ammunition clips. As indicated above, the jury found Sogomonian guilty on Count 1 (possession of the 9 millimeter pistol after having been convicted of a crime with a potential sentence exceeding one year in prison) and was unable to reach a verdict on Counts 2 and 3, which both related to the .25 caliber pistol. Counts 2 and 3 were dismissed. On appeal, Sogomonian claims that (1) the district court’s instruction to the jury on reasonable doubt was unconstitutional, (2) the district court committed plain error when it gave a conscious avoidance instruction to the jury, and (3) the district court committed plain error in selecting alternate jurors by lottery at the conclusion of the trial in violation of Federal Rule of Criminal Procedure 24(c).

II. DISCUSSION

A. The District Court’s Reasonable Doubt Instruction

Sogomonian argues that the district court’s instruction to the jury on reasonable doubt was unconstitutional for four reasons. First, Sogomonian claims that, by equating a reasonable doubt with a fair doubt, the trial court created confusion as to the definition of reasonable doubt. Second, appellant suggests that the reasonable doubt instruction was unconstitutional because it told jurors that they would not be determining whether Sogomonian was guilty or not guilty. Third, Sogomonian argues that the district court “eviscerated the presumption of innocence,” “applied unfair pressure” to the jurors, and “diluted the government’s burden of proof’ when it told jurors that they were obligated to explain their views to each other and to the court. Finally, Sogomonian argues that, as a whole, these deficiencies in the district court’s instruction create a reasonable likelihood that the jury was misled and confused by the instructions.

With respect to reasonable doubt instructions, the Supreme Court has held that “so long as the court instructs the jury on the necessity that the defendant’s guilt be proved beyond a reasonable doubt, see Jackson v. Virginia, 443 U.S. 307, 320 n. 14, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979), the Constitution does not require that any particular form of words be used in advising the jury of the government’s burden of proof. Cf. Taylor v. Kentucky, 436 U.S. 478, 485-86, 98 S.Ct. 1930, 56 L.Ed.2d 468 (1978). Rather, ‘taken as a whole, the instructions [must] correctly conve[y] the concept of reasonable doubt to the jury.’ Holland v. United States, 348 U.S. 121, 140, 75 S.Ct. 127, 99 L.Ed. 150 (1954).” Victor v. Nebraska, 511 U.S. 1, 5, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994). When considering the district court’s reasonable doubt instruction, this Court does “not engage in an inquiry of harmless error review.” United States v. Doyle, 1.30 F.3d 523, 536 (2d Cir.1997). Instead, this Court must “assess only the charge, taken as a whole, in order to determine whether there is a reasonable likelihood that the jury misinterpreted the reasonable doubt instruction. ... Here, therefore, we need *352 only decide whether there is a reasonable likelihood that the jury misunderstood the reasonable doubt standard.” Id. (emphasis in original). In addition, this Court must focus on the cumulative effect of the definitions of reasonable doubt given by the district court. See Gaines v. Kelly, 202 F.3d 598, 606 (2d Cir.2000). Considering the district court’s reasonable doubt instruction and the jury charge as a whole and considering the potential cumulative effect of the alleged errors, we hold that there is not a reasonable likelihood that the jury misinterpreted or misunderstood the reasonable doubt instruction. Therefore, we hold that the district court’s reasonable doubt instruction was constitutional.

B. The District Court’s Conscious Avoidance Instruction

Sogomonian argues that his conviction should be overturned based on the conscious avoidance instruction included in the jury charge. We review this claim under a plain error standard because So-gomonian did not object to the conscious avoidance charge at trial. A finding of plain error requires this Court to rule that the district court made a mistake that is clear and obvious, “affected substantial rights,” and “seriously affects the fairness, integrity or public reputation of judicial proceedings.” Johnson v. United States, 520 U.S. 461, 469, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997); see also United States v. Martinez-Rios, 143 F.3d 662, 676 (2d Cir.1998). Although the government concedes that it was a mistake to include the conscious avoidance language in the jury charge, Sogomonian does not make the necessary showing that his “substantial rights” were affected. He only makes allegations of jury confusion, and therefore, we hold that the district court’s mistake does not rise to the level of plain error.

C. The District Court’s Selection of Alternate Jurors

Sogomonian argues that his conviction should be overturned because the district court selected alternate jurors by lottery at the conclusion of the trial in violation of Federal Rule of Criminal Procedure 24(c). Specifically, Sogomonian argues that the lottery method used (1) does not conform with the requirement that alternate jurors replace regular jurors “in the order called” and (2) does not ensure that the additional peremptory challenge provided for by Rule 24(c)(2) is used for the removal of an alternate juror. The government concedes that the district court “was not in strict compliance” with Rule 24(c) when it selected the alternate jurors by lottery, but maintains that any error committed by the district court was harmless. Again, we review for plain error because Sogomonian did not object at trial.

At the commencement of the trial, the district court selected fourteen jurors using the struck method. Under this method, thirty-two venire persons were questioned. After the venire persons were cleared for' cause, the parties exercised their peremptory challenges. Pursuant to Federal Rules of Criminal Procedure 24(b) and 24(c)(2), the defendant was allowed eleven peremptory challenges and the government was allowed seven. After the eighteen peremptory challenges had been used, fourteen venire persons remained. The district court empaneled all fourteen remaining venire persons as the “trial jury” without designating the alternate jurors. At the close of the trial, after instructing the jury on the law, Judge Elf-vin, by lottery, and without objection from either party, drew the numbers of two of the fourteen jurors out of a box. The two alternate jurors chosen at random did not participate in the deliberations.

*353 This Court has not addressed the issue of choosing alternate jurors by lottery pri- or to the commencement of deliberations. We have cautioned that “[t]he absence of benefit being so clear and the danger of prejudice so great, it seems foolhardy to depart from the command of Rule 24.” United States v. Hayutin, 398 F.2d 944, 950 (2d Cir.), cert. denied, 393 U.S. 961, 89 S.Ct. 400, 21 L.Ed.2d 374 (1968). We have also held that Rule 24(c) “represents a national consensus of bench and bar and ought not be disturbed on a local level.” United States v. Viserto, 596 F.2d 531, 540 (2d Cir.1979) (affirming conviction after parties stipulated to the district court empaneling sixteen jurors without designating regular and alternate jurors and allowing the parties to select jurors to be discharged until the requisite number of regular jurors remained).

Other federal appellate courts considering the actions of district courts that have not applied Rule 24(c) as it is drafted have concluded that, although not encouraged, such error is harmless. In United States v. Brewer, 199 F.3d 1283, 1286-87 (11th Cir.2000), the Eleventh Circuit faced a virtually identical factual scenario and concluded that the district court’s error was harmless. See also United States v. Love, 134 F.3d 595, 601-03 (4th Cir.) (finding no prejudice to the defendant when, over the defendant’s objection, eighteen jurors were initially chosen without designation as to their regular or alternate status and six jurors were eliminated at random prior to deliberations), cert. denied, 524 U.S. 932, 118 S.Ct. 2332, 141 L.Ed.2d 705 (1998); United States v. Olano, 62 F.3d 1180, 1190 n. 3 (9th Cir.1995) (finding no prejudice to defendant when the district court waited until just before the beginning of jury deliberations to designate the alternate jurors); United States v. Sivils, 960 F.2d 587, 593-94 (6th Cir.1992) (finding no prejudice to defendants where district court employed seemingly identical process as seen in the case before the bar); United States v. Aguon, 851 F.2d 1158, 1171 (9th Cir.1988) (en banc) (finding no prejudice to defendant when the district court waited until just before the beginning of jury deliberations to designate the alternate jurors), overruled on other grounds, Evans v. United States, 504 U.S. 255, 112 S.Ct. 1881, 119 L.Ed.2d 57 (1992). Therefore, based on the reasoning of our sister circuits and Sogomonian’s failure to show that his substantial rights were affected by the district court’s use of a lottery system to select alternate jurors, we reject Sogo-monian’s argument that his conviction should be overturned because of the district court’s failure to adhere to the letter of Federal Rule of Criminal Procedure 24(c).

III. CONCLUSION

We have considered all of appellant’s arguments and find them to be unpersuasive. Therefore, we uphold Sogomonian’s conviction, and the judgment of the district COUrt ÍS AFFIRMED.

Notes

. 18 U.S.C. § 922(g)(1) makes it illegal for an individual who has previously been convicted of a crime punishable by imprisonment for a term exceeding one year to possess a firearm. 18 U.S.C. § 922(k) makes it illegal to possess a firearm that has had its Manufacturers Serial Number removed or obliterated. The relevant portion of 18 U.S.C. § 924 is as follows: (a)(1) Except as otherwise provided in this subsection, subsection (b), (c), or (f) of this section, or in section 929, whoever — (A) knowingly makes any false statement or representation with respect to the information required by this chapter to be kept in the records of a person licensed under this chapter or in applying for any license or exemption or relief from disability under the provisions of this chapter; (B) knowingly violates subsection (a)(4), (f), (k), (r), (v), or (w) of section 922; (C) knowingly imports or brings into the United States or any possession thereof any firearm or ammunition in violation of section 922(1); or (D) willfully violates any other provision of this chapter, shall be fined under this title, imprisoned not more than five years, or both. (2) Whoever knowingly violates subsection (a)(6), (d), (g), (h), (i), (j), or (o) of section 922 shall be fined as provided in this title, imprisoned not more than 10 years, or both.