
62 P.3d 444 (2002)
2002 UT 118
STATE of Utah, Plaintiff and Appellee,
v.
Spencer E. HOUSKEEPER, Defendant and Appellant.
Nos. 20000059, 20010314.
Supreme Court of Utah.
December 10, 2002.
*446 Mark L. Shurtleff, Att'y Gen., Laura B. Dupaix, Asst. Att'y Gen., Salt Lake City, Sherry Ragan, Provo, for plaintiff.
Michael D. Esplin, Margaret P. Lindsay, Provo, for defendant.
WILKINS, Justice:
¶ 1 Defendant, a minor, was charged in juvenile court with aggravated sexual assault and forcible sodomy. The case was transferred to the district court pursuant to section 78-3a-602 of the Utah Code, the "Serious Youth Offender Statute," where the defendant was convicted of attempted rape. On appeal, defendant contends that (1) the district court erred in instructing the jury on rape and attempted rape as lesser included offenses of aggravated sexual assault, (2) the case should have been remanded to the juvenile court for sentencing, (3) the juvenile court erred in binding the case over to district court initially, and (4) the district court admitted evidence of other bad acts contrary to rule 404(b) of the Utah Rules of Evidence. We affirm.

BACKGROUND
¶ 2 We present the facts in the light most favorable to the jury's verdict. See, e.g., State v. Evans, 2001 UT 22, ¶ 2, 20 P.3d 888. On November 8, 1997, defendant, Spencer Houskeeper, and the victim, J.S., were among a group of teenagers who gathered at the home of A.B. to "hang out." Several of the teenagers took controlled pain medication and muscle relaxants for recreational purposes. Spencer and the victim spoke with each other and later engaged in some kissing in the bathroom. Later, the two left A.B.'s home together and drove a short distance to a church parking lot where they engaged in sexual activity. The encounter included a number of sexual acts including an attempt by defendant to have intercourse with the victim without her consent. The incident resulted in charges of aggravated sexual assault and forcible sodomy in the juvenile court.
¶ 3 After a preliminary hearing, the juvenile court concluded that there was probable cause to believe that defendant had committed the crimes. The juvenile court also concluded that defendant failed to prove one of the three statutory requirements necessary for the juvenile court to retain jurisdiction under the Serious Youth Offender Statute, specifically section 78-3a-602(3)(b). According to the statute, in order to be retained in juvenile court, the defendant must prove by clear and convincing evidence that:
(i) the minor has not been previously adjudicated delinquent for an offense involving the use of a dangerous weapon which would be a felony if committed by an adult;
(ii) that if the offense was committed with one or more other persons, the minor appears to have a lesser degree of culpability than the codefendants; and
(iii) that the minor's role in the offense was not committed in a violent, aggressive, or premeditated manner.
Utah Code Ann. § 78-3a-602(3)(b)(1996). The State and defendant stipulated that the first two subsections were not applicable in this case. The court concluded that defendant failed to prove that the offense was not committed violently or aggressively as evidenced by the injuries sustained by the victim. Accordingly, the case was bound over to the district court for trial. Defendant appealed the bind-over order to the court of appeals, but later filed a motion to voluntarily dismiss the appeal, which the court of appeals granted.
¶ 4 Subsequently, in district court, defendant filed a motion to quash the bind-over order. Defendant asserted that the state had failed to establish the elements of aggravated sexual assault and that Utah's Serious Youth Offender Statute was unconstitutional. The district court denied his motion. Defendant petitioned this court for interlocutory *447 review of that decision. That petition was denied.
¶ 5 Prior to trial, defendant filed a motion in limine to exclude evidence of prior bad acts and a stipulation was entered regarding the motion. Although no written stipulation appears in the record, both parties appear to have agreed that the evidence would not be introduced unless defendant first "opened the door" in his testimony. During her testimony, the victim recounted statements made by her friend, A.D., implying prior sexual misconduct by the defendant with A.D. Pursuant to the stipulation, counsel for the defendant moved for a mistrial. The court denied the motion but instructed the jury that the evidence was inadmissible.
¶ 6 Defendant testified that he had never had sexual intercourse before. During cross-examination, the prosecution asked if defendant had ever engaged in oral sex. Defendant objected. The court found that, despite defendant's testimony that he had never had sexual intercourse before, prior acts of oral sex were inadmissible because they were more prejudicial than probative.
¶ 7 During cross-examination, defendant admitted to a phone conversation with A.D. After defendant's testimony, the prosecution called A.D. as a rebuttal witness. The defense objected to her testimony regarding the substance of the phone conversation between her and the defendant. The judge indicated that he was inclined to allow the evidence on the basis that defendant had opened the door in his testimony. The defense conceded that testimony regarding defendant's attempt to influence the witness went to credibility, but objected to testimony from A.D. concerning any prior sexual misconduct of the defendant. The court allowed the evidence.
¶ 8 Defendant's counsel also objected to the testimony implicating the defendant in soliciting drugs from A.B. six weeks prior to the incident. The objection was apparently overruled in a bench conference. Defendant's counsel later entered an objection on the record.
¶ 9 Prior to deliberations, the district court, over defendant's objection, instructed the jury on rape and attempted rape as lesser included offenses of aggravated sexual assault. The jury convicted defendant of attempted rape.
¶ 10 Subsequently, defendant filed a motion to arrest judgment, arguing, inter alia, that the jury instructions on rape and attempted rape were improper. That motion was denied. Defendant appeals.

ANALYSIS

I. LESSER INCLUDED OFFENSES
¶ 11 Defendant first contends that the jury was improperly instructed on the crimes of rape and attempted rape as lesser included offenses of the crime of aggravated sexual assault. He argues that rape and attempted rape are not necessarily included in the offense of aggravated sexual assault. Whether a jury instruction correctly states the law presents a question of law which we review for correctness. State v. Archuleta, 850 P.2d 1232, 1244 (Utah 1993).
¶ 12 Section 76-1-402(3) of the Utah Code specifies that an offense is included in the charged offense if "[i]t is established by proof of the same or less than all the facts required to establish the commission of the offense."[1] Defendant relies on our statement in State v. Baker, 671 P.2d 152 (Utah 1983), that in order to qualify as a lesser included offense, "the offense[ ] must be such that the greater cannot be committed without necessarily having committed the lesser." Id. at 156. Defendant argues that, since aggravated sexual *448 assault[2] can be committed during the course of a number of crimes not limited to rape and attempted rape, the crimes of rape and attempted rape are not necessarily included in the crime of aggravated sexual assault.
¶ 13 It is true that the relationship between a lesser included offense and the charged offense will generally be such that the greater cannot be committed without committing the lesser. However, in State v. Hill, 674 P.2d 96 (Utah 1983), we noted that offenses similar to aggravated sexual assault, which can be committed in the course of a variety of lesser offenses, are an exception. Id. at 97. In those cases, the court must determine whether the lesser offense is necessarily included in the specific variation of the greater offense proved by the evidence at trial. Id. Thus, in Hill, while theft was not necessarily included in all variations of aggravated robbery, it was held to be necessarily included in, and thus a lesser included offense of, the variation of aggravated robbery which had been proved in that case. Id. at 97-98.
¶ 14 Furthermore, the interpretation defendant urges us to adopt is contrary to the policy justifications underlying the legal doctrine of lesser included offenses. Originally, the doctrine existed at common law to allow the prosecution to seek a conviction in circumstances where the evidence proved criminal activity but failed to establish one of the elements of the charged crime. See Beck v. Alabama, 447 U.S. 625, 633, 100 S.Ct. 2382, 65 L.Ed.2d 392 (1980). As this court has stated, "when evidence of a defendant's criminal conduct has been placed before a court of justice, even though that conduct has not been specifically charged, it would be a mockery of our criminal laws for a court to ignore a proved crime and acquit on the charged crime." State v. Howell, 649 P.2d 91, 95 (Utah 1982).
¶ 15 At the same time, the accused has a constitutional right to be informed of the charges against him and to have an adequate opportunity to prepare a defense. See Baker, 671 P.2d at 155-56; Howell, 649 P.2d at 95. Allowing the prosecution to introduce a new and unrelated charge at the jury instruction phase of trial would effectively abrogate those rights. Therefore, the critical inquiry for determining the propriety of an instruction submitted by the prosecution was correctly stated in Howell: "[A] trial court may properly give a lesser included offense instruction, even over a defendant's objection, if there is clearly no risk that the defendant will be prejudiced by lack of notice and preparation so as to deprive him of a full and fair opportunity to defend himself." Howell, 649 P.2d at 95.
¶ 16 In the instant case, the information clearly stated that the aggravated sexual assault with which the defendant was charged took place during the commission of a rape or attempted rape. Further, the evidence introduced by the defendant at trial demonstrates that he was aware of these lesser included offenses, and had a full and fair opportunity to defend against them. Accordingly, we find no error in the jury instruction on rape and attempted rape.

II. TUNZI AS PRECEDENT
¶ 17 Alternatively, defendant contends that even if the instructions on lesser included offenses were proper, it was improper to sentence defendant in district court upon a conviction for one of those offenses. Defendant relies on State v. Tunzi, 2001 UT App 224, 31 P.3d 588. In that case, the court of appeals held that the Serious Youth Offender Statute requires that the juvenile *449 court regain jurisdiction of a defendant if he is not convicted of the offense which qualified him for adult jurisdiction. We review the district court's interpretation of the Serious Youth Offender Statute for correctness, see State v. Galli, 967 P.2d 930, 933 (Utah 1998), and conclude that the Tunzi case is incorrect on this issue.
¶ 18 We acknowledge that the statutory language defining the jurisdiction of the district court over a serious youth offender is not a model of clarity.[3] Under section 78-3a-603(12), once a minor has been bound over to the district court under the Serious Youth Offender Statute, the jurisdiction of the juvenile court over that individual is terminated regarding "that offense, any other offenses arising from the same criminal episode, and any subsequent misdemeanors or felonies charged against him." Section 78-3a-602(7) provides for the trying of all such offenses in district court upon a finding of probable cause. Taken by themselves, these subsections would indicate that once a juvenile has been bound over to district court to answer a serious youth offender charge, that juvenile has lost the benefits of the juvenile system for all time. However, section 78-3a-602(10) clearly indicates the intent of the legislature that if there is a favorable disposition of all charges against him in district court, the juvenile offender should once again be eligible for the benefits of the juvenile system.[4]
¶ 19 In Tunzi the court of appeals asserted that the charges spoken of in section 78-3a-602(10) must only indicate the charges for which the juvenile was originally required to be bound over to district court. 2001 UT App 224 at ¶ 18, 31 P.3d 588. The court reasoned that allowing a defendant to be convicted and sentenced in the adult system for a lesser offense would be contrary to the purpose of the Serious Youth Offender Statute, which the court interpreted to be the identification of certain crimes indicating a juvenile to be "just as dangerous as adult criminals," from whom the public needs special protection. Id. (quoting In re A.B., 936 P.2d 1091, 1098 (Utah Ct.App.1997)).
¶ 20 The Serious Youth Offender Statute, however, is not intended to absolutely delimit the types of crimes for which a juvenile may be held to answer in district court. Indeed, the Serious Youth Offender Statute limits the discretion of the juvenile court over certain enumerated offenses for which it "shall order that the defendant be bound over." § 78-3a-602(3)(b). A juvenile may also be certified to stand trial in district court at the discretion of the juvenile judge under section 78-3a-603. Thus, the purpose of the statute is simply to define the manner in which such charges will be disposed. If the legislature had intended to protect a juvenile from being convicted of a lesser crime, there is no reason for the language in section 78-3a-602(7) and section 78-3a-603(12) transferring jurisdiction of all episodic and future crimes to the district court. This language instead denotes the usual concern for judicial economy in disposing of the charges against a defendant.
¶ 21 Moreover, as Judge Orme pointed out in his concurring opinion in Tunzi, adopting the interpretation of the court of appeals requires the transfer of the case back to the juvenile court with no procedural guidelines, and sentencing by a judge who did not preside over the case. 2001 UT App 224 at ¶ 24, 31 P.3d 588 (Orme, J., concurring). We find no evidence supporting such an "aberrational approach to criminal jurisprudence," id., in the plain language of the Serious Youth Offender Statute prior to its recent amendment by the Utah State Legislature. Indeed, we note that the amendment to section 78-3a-602,[5] intended to clarify the *450 meaning of the original language, confirms this interpretation.
¶ 22 We conclude that a plain reading of the original language of the Serious Youth Offender Statute requires that once a juvenile has been bound over to district court for an offense enumerated in that statute, the district court has jurisdiction to try that offense, any offense arising out of the same episode, or any subsequent offense. The juvenile court potentially regains jurisdiction over the individual only after the juvenile has been acquitted of, found not guilty of, or has had all such charges against him dismissed. To the extent that Tunzi is to the contrary, it is incorrect.

III. JUVENILE COURT'S BIND-OVER ORDER
¶ 23 The defendant next alleges error in the juvenile court's original bind-over order. Because the bind-over order was not timely appealed, we have no jurisdiction to hear challenges to the order. Bind-over orders are final, appealable orders. See M.C. v. State, 916 P.2d 914, 916 (Utah Ct. App.1996) (holding that a bind-over order is a final, appealable order because it terminates the jurisdiction of the juvenile court); see also State v. Bell, 785 P.2d 390, 406 (Utah 1989) (stating that where an order terminates jurisdiction of juvenile court, such order is final and appealable); In re Atcheson, 575 P.2d 181, 183 (Utah 1978) (stating that where an order terminates jurisdiction of juvenile court, such order is final). Pursuant to rule 4 of the Utah Rules of Appellate Procedure, a notice of appeal must be "filed with the clerk of the trial court within thirty days after the date of entry of the judgment or order appealed from." Utah R.App. 4(a). Failure to timely file an appeal pursuant to rule 4 constitutes a waiver of the right to appeal. Additionally, failure to timely file deprives an appellate court of jurisdiction over the appeal. Reisbeck v. HCA Health Servs. of Utah, Inc., 2000 UT 48, ¶ 5, 2 P.3d 447; see also Bell, 785 P.2d at 406 ("[B]ecause no appeal was taken from this final order ... we do not reach the merits of defendant's present contentions."). Here, while defendant timely filed a notice of appeal of the bind-over order with the court of appeals, he voluntarily withdrew the appeal, which was ordered dismissed by the court of appeals. Consequently, defendant waived his right to appeal the bind-over order, and we have no jurisdiction to consider his contentions.

IV. ADMISSION OF PRIOR BAD ACT EVIDENCE
¶ 24 Defendant's final contention is that the trial court erred in admitting evidence of his prior bad acts, thereby prejudicing the finder of fact against him. Rule 404(b) of the Utah Rules of Evidence precludes evidence of other bad acts by the defendant if its sole purpose is to imply that the defendant has bad character and a disposition to commit the charged offense. This rule works in conjunction with rules 402 and 403 to ensure that a defendant is only convicted because he committed the charged offense and not because the jury is convinced of his cumulative bad behavior. Under these rules, defendant challenges the admission of evidence implicating him in soliciting drugs from A.B. several weeks prior to the incident and the admission of A.D.'s testimony regarding a prior non-consensual sexual encounter. In conjunction with the second challenge, defendant charges counsel for the state with prosecutorial misconduct in her characterization of A.D.'s testimony in her summation. We treat these challenges separately.
¶ 25 Defendant asserts that there could be no probative value to the drug solicitation evidence because it was irrelevant to the sexual encounter between himself and the victim. He argues that the only possible purpose for admitting the evidence would be to convince the jury of his bad character. However, there is ample evidence properly in the record both that the defendant had taken drugs the night of the incident and that the defendant had brought his own supply. If *451 the drugs defendant was attempting to obtain from A.B. were commonly associated with the commission of rape, that evidence might have been quite probative. When the witness testified that he did not recall the type of drugs the defendant had solicited, the judge promptly ended that line of questioning, indicating that he was aware of and sensitive to both the potential probative and prejudicial effects of the testimony.
¶ 26 Moreover, even if we assume that the evidence was improper, an appellate court will not overturn a jury verdict for the admission of improper evidence if the admission of the evidence did not reasonably effect the likelihood of a different verdict. See State v. Hamilton, 827 P.2d 232, 240 (Utah 1992); State v. Featherstone, 781 P.2d 424, 431 (Utah 1989). Considering the evidence of drug use and possession already properly in the record, the suggestion that defendant had attempted to obtain drugs, once upon a time, would come as little surprise to the jury, and would do little to prejudice the jury against him. We therefore find that admission of the drug solicitation evidence was, at most, harmless error.
¶ 27 The second challenge involves the admission of A.D.'s testimony regarding a prior non-consensual sexual encounter between herself and the defendant. Rule 404(b) does not, however, categorically preclude the admission of other bad acts evidence. Rather, it stands for the principle that such evidence is only admissible "if it is relevant for a non-character purpose and meets the requirement of Rules 402 and 403." Utah R. Evid. 404 advisory committee note; see also State v. Fedorowicz, 2002 UT 67, ¶ 25, 52 P.3d 1194.
¶ 28 A.D.'s testimony was admitted for the legitimate purpose of impeaching defendant's credibility. While rule 404(b) lists examples of some of the legitimate purposes for which other bad acts evidence may be admitted, the list is not exhaustive. See State v. Ramirez, 924 P.2d 366, 369 (Utah 1996). It is well settled that when a defendant waives his right not to testify, his testimony, like that of any other witness, is subject to being impeached by cross-examination or by rebuttal evidence. State v. Wells, 603 P.2d 810, 812 (Utah 1979). Evidence for the purpose of impeaching credibility may be admissible even if it introduces evidence of a prior bad act. State v. Tucker, 800 P.2d 819, 824 (Utah Ct.App.1990). In this case, defendant had spoken with A.D. outside of court during the course of the trial about her testimony. When asked about this conversation, defendant characterized it as an innocent inquiry about A.D.'s testimony if she were called, and claimed not to know that she had been subpoenaed to testify as a witness. By so testifying, defendant opened the door, and A.D.'s testimony was intended for the legitimate purpose of impeaching defendant's characterization of their conversation.
¶ 29 Even if evidence is intended for a proper purpose, it must also meet the requirements of rules 402 and 403. Rule 402 requires that evidence be relevant. Evidence is relevant if it tends "to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence." Fedorowicz, 2002 UT 67 at ¶ 32, 52 P.3d 1194. The state's questioning of Houskeeper on cross-examination about his conversation with A.D., and A.D.'s rebuttal testimony, were relevant to establishing the defendant's credibility.
¶ 30 Rule 403 requires that evidence be excluded, even if relevant, if "its probative value is substantially outweighed by the danger of unfair prejudice." Utah R. Evid. 403. A.D.'s testimony focused on her characterization of the conversation which took place between herself and the defendant. The prosecution refrained from questioning A.D. about the prior incident beyond those facts pertinent to her characterization of that conversation. Thus, the potential prejudicial effect of the testimony was minimized and certainly did not "substantially outweigh" the importance of the testimony to the probative question of credibility. The treatment of the evidence by the prosecution in summation was also directed to the issue of defendant's credibility. We therefore find no error in the district court's decision to admit A.D.'s testimony, and no prosecutorial misconduct *452 in the prosecutor's treatment of the evidence in summation.

CONCLUSION
¶ 31 The trial court properly instructed the jury on the crimes of rape and attempted rape as lesser included offenses of the crime of aggravated sexual assault. The trial court had jurisdiction to try the defendant on any offenses arising out of the original criminal episode. Defendant waived his right to appeal the bind-over order by not appealing it within thirty days. Lastly, the trial court did not err in admitting testimony from A.D. or from A.B. and we find no misconduct in the prosecutor's treatment of testimony. We therefore affirm the trial court.
¶ 32 Chief Justice DURHAM, Associate Chief Justice DURRANT, Justice HOWE, and Justice RUSSON concur in Justice WILKINS' opinion.
NOTES
[1]  This court has described this standard, often referred to as the "necessarily included offense" standard in the following ways: "The lesser offense must be a necessary element of the greater offense and must of necessity be embraced within the legal definition of the greater offense and be a part thereof," State v. Woolman, 84 Utah 23, 36, 33 P.2d 640, 645 (1934), "no element may be included in the lesser offense that is not included in the greater offense," State v. Howell, 649 P.2d 91, 95 (Utah 1982), and "both the legal elements and the actual evidence or inferences needed to demonstrate those elements must necessarily be included within the original charged offense." State v. Baker, 671 P.2d 152, 156 (Utah 1983).
[2]  The crime of aggravated sexual assault is set forth in Utah Code section 76-5-405(1), which reads:

A person commits aggravated sexual assault if in the course of a rape or attempted rape, object rape or attempted object rape, forcible sodomy or attempted forcible sodomy, or forcible sexual abuse or attempted forcible sexual abuse the actor:
(a) causes bodily injury to the victim;
(b) uses or threatens the victim with use of a dangerous weapon as defined in Section 76-1-601;
(c) compels, or attempts to compel, the victim to submit to rape, object rape, forcible sodomy, or forcible sexual abuse, by threat of kidnaping, death, or serious bodily injury to be inflicted imminently on any person; or
(d) is aided or abetted by one or more persons.
[3]  Language defining the jurisdiction of the district court in the case of a serious youth offender is found in the Utah Code in sections 78-3a-602(7), 78-3a-602(10) (renumbered 78-3a-602(11)(2002)), and 78-3a-603(12) and (14).
[4]  Section 78-3a-602(10) (1996) is not superfluous language as was suggested by the Tunzi court. 2001 UT App 224 at ¶ 25, 31 P.3d 588, (Orme, J., concurring).
[5]  The legislature amended section 78-3a-602 effective February 27, 2002, adding another subsection to include the following language: "If a minor enters a plea to, or is found guilty of, any of the charges filed or any other offenses arising from the same criminal episode, the district court retains jurisdiction over the minor for all purposes, including sentencing." Utah Code Ann. § 78-3a-602(10) (Supp.2002).
