ROVNER, Circuit Judge.

A jury convicted Robert Smith of (1) possessing an unregistered explosive device, see 26 U.S.C. § 5861(d); (2) constructing a destructive device without paying taxes, see 26 U.S.C. § 5861(f); (3) attempting to use an explosive device to destroy a place of business, see 18 U.S.C. § 844(i); and (4) carrying a pipe bomb while committing a crime of violence, see 18 U.S.C. § 924(c)(1)(A). The district court sentenced him to concurrent 120-month terms of imprisonment on the first three counts and to a 30-year term on the fourth count to run consecutively to the 120-month terms. Smith now challenges various rulings of the district court, arguing that the cumulative effect of what he believes are errors tainted the jury. Smith also argues that application of the 30-year mandatory consecutive sentence for using a pipe bomb constitutes cruel and unusual punishment and violates his Fifth Amendment right to be put in jeopardy only once for the same offense. We affirm.

I.

On the morning of July 3, 2003, the office manager at an Allstate insurance agency in Crest Hill, Illinois, found a box outside of the agency. The Federal Express label on the box was addressed to Leo Bick, the agency's owner and the boy-friend of Smith's former girlfriend. The office manager brought the box inside and, later that morning when Bick arrived at work, he opened it. He heard a snap, saw wires hanging from the box, and pulled a bottle of gasoline out of the box. Fearing that the package contained an explosive device, he carried it and the bottle of gasoline outside and called the police. Members of the DuPage County Bomb Squad inspected the package, x-rayed it, determined that it contained a pipe bomb, and deactivated the bomb.

The bomb was comprised of a steel pipe held together by two end caps with a metal rod connecting the end caps. Inside of the pipe was a plastic bag containing various types of explosive powder and an igniter. A thumb print, later identified as Smith's, was found on the plastic bag. A set of wires linked the igniter to a mousetrap which in turn was connected to two batteries. The mousetrap was set to close onto a copper plate when the box was opened, completing a circuit and triggering an explosion. The bomb also contained various forms of shrapnel including shotgun shell primers, construction staples, roofing nails, and lead shot. A bottle of gasoline was inside the box next to the bomb. The components were held together with tape, on which a single human hair, later discovered to match Smith's, was found. After a year-long investigation that involved local police and the Bureau of Alcohol, Tobacco, Firearms, and Explosives, Smith was arrested and charged with constructing, possessing, and attempting to use an explosive device.

The district court appointed a fingerprint expert to assist in Smith's defense. The expert reviewed the fingerprint evidence acquired during the investigation and concurred with the government that the print found on a plastic bag inside the pipe bomb was Smith's. The defense moved to require the government to give the defense expert access to the bomb components and packaging for further testing and requested that the government provide fingerprint exemplars for the investigating officers and potential suspects. At a hearing on Smith's motion, the government asserted that there were no fingerprints found on the bomb components or packaging, other than the thumb print found on the plastic bag. Because the Federal Express label on the package had not yet been tested, the government agreed to test it. At Smith's request, the government also agreed to reexamine the rest of the evidence to ensure that no new prints had become visible. The district court then denied Smith's motion without prejudice because there were no finger-prints for the expert to examine, but indicated that it would be willing to revisit its decision if further fingerprints were found. Three fingerprints that did not match Smith's were later found on the Federal Express label, but Smith did not renew his motion.

At Smith's jury trial, the government presented scientific and circumstantial evidence linking Smith to the bomb. A fingerprint expert testified that Smith's thumb print was found on a plastic bag containing explosive powder inside of the bomb, a conclusion that Smith did not contest. Another expert testified that the mitochondrial DNA in the hair stuck to the tape that held the bomb together matched Smith's DNA, and Smith did not argue that this conclusion was incorrect. The government's evidence also showed that Smith rented a post office box at the post office where the Federal Express label on the box originated. A retired agent from the Bureau of Alcohol, Tobacco, Firearms, and Explosives testified that after Smith was arrested, he admitted that he had handled the type of mousetrap that was used in the bomb. Additionally, some of the shotgun shell primers in the bomb, which according to the government's witness had not been made since the 1950s, matched primers in shotgun shells found at Smith's house.

The evidence also showed that Smith and Bick loathed each other. The acrimony seems to have begun after Bick began dating Smith's ex-girlfriend, Lisa Kehr. Witnesses for both the government and the defense testified that Smith and Bick engaged in multiple verbal confrontations, and Bick testified that Smith once punched him. Government witnesses testified that Smith threatened to "break" Bick "financially and physically" and once referred to Bick as "a dead man." Over Smith's objection, the government introduced a photograph, taken by Bick, of Smith making an obscene gesture directed at Bick. Smith later testified that he made the gesture only in response to an obscene gesture made by Bick.

The government elicited the testimony of an explosives expert, who first described how the bomb was constructed. The expert analyzed the pieces of the dismantled pipe bomb and built a model to show what the fully constructed bomb looked like. Using the model, he then performed a brief demonstration, to which Smith's attorney objected, to illustrate how the bomb was intended to function. He also opined that the intended explosion did not occur because either there was a flaw in the electrical connection or a short in the igniter. He concluded that the bomb was designed to maim and kill bystanders and to destroy property.

Smith elected to testify and denied having anything to do with the bomb. On cross-examination, the government used two letters to impeach his credibility. The first letter was written by Smith, while he was in pretrial detention, to Robert Ishmael, Smith's friend and former boss. Smith testified that he told the ATF agent who questioned him that he had never handled the type of mousetrap used in the bomb. In the letter, Smith wrote that he told the ATF agent that he did not remember whether or not he handled the mouse-traps. Smith addressed the letter to "ATTNY Robert Ishmael," however Ishmael is not an attorney, and, although Ishmael is a private investigator, he was not retained by Smith's lawyer to work on Smith's behalf. At trial, Smith's attorney did not object to the government's use of the letter and stated that he did not believe that it was privileged under the work-product doctrine.

The government also impeached Smith with a letter he wrote, but did not mail, to Kehr. Smith had testified that, at the time of the attempted bombing, he no longer had feelings for Kehr, but, in the letter, dated about two months prior to the incident, he wrote, "My heart will always be with you" and "I will remember your intimate words every day." The government did not turn the letter over to the defense during discovery, but Smith's attorney did not object to the government's use of the letter at trial. At a post-trial hearing, Smith's attorney indicated that he chose not to object because he believed that the letter was helpful to the defense.

Ultimately, the jury convicted Smith on all four counts, and the judge sentenced him to three concurrent 120-month sentences and a statutorily-mandated 30-year sentence to run consecutive to the 120-month sentences.

II.

On appeal Smith argues that the district court erred in (1) denying his motion to allow his fingerprint expert access to evidence and to require the government to provide fingerprint exemplars of individuals related to the investigation; (2) admitting the photo of Smith making an obscene gesture; (3) allowing the government's expert to use a model to demonstrate how the actual bomb was intended to function; (4) permitting the government to impeach Smith with a letter that Smith wrote to his friend; and (5) permitting the government to impeach Smith with the letter he wrote but did not send to Kehr. Smith also contends that the cumulative effect of these errors tainted the jury's verdict. We address each issue in turn.

A. Smith's Fingerprint Expert

Smith first argues that the district court erred in denying his motion seeking fingerprint exemplars of the investigators and potential suspects and requesting access to the bomb components. He contends that the presence of only a single thumb print on the plastic bag is inconsistent with the way that a person holds a plastic bag and thus indicates that someone might have planted this evidence to frame him. He asserts that access to the bomb components and exemplars was necessary to help him advance his theory and that the district court's ruling effectively denied him access to a fingerprint expert.

We review for abuse of discretion a district court's denial of a defendant's request for expert services. See United States v. King, 356 F.3d 774, 778 (7th Cir. 2004). The government will give an indigent defendant access to expert services adequate to facilitate the defendant's representation if the court finds that the services are necessary. See 18 U.S.C. § 3006A(e)(1). Expert services should be provided where "a reasonable attorney would engage such services for a client having the independent financial means to pay for them." United States v. Cravens, 275 F.3d 637, 639 (7th Cir. 2001) (quoting United States v. Alden, 767 F.2d 314, 318 (7th Cir. 1984)). However, when a defendant requests the assistance of an expert, the district court may consider whether the defendant has a "plausible defense" before granting the request. See King, 356 F.3d at 778; Cravens, 275 F.3d at 639. And the district court need not order expert assistance if doing so amounts to a "fishing expedition." See King, 356 F.3d at 778.

Here, Smith received access to an adequate fingerprint expert. The district court appointed a fingerprint expert to assist in Smith's defense. The expert examined the thumb print found on the plastic bag inside of the bomb and concluded the print was Smith's. At the time Smith made his motion seeking access to the bomb components and fingerprint exemplars, no other usable fingerprints had been found. Thus, there was nothing against which to compare the requested exemplars and no reason for the expert to examine evidence that did not contain fingerprints. It was within the district court's discretion to conclude that Smith's request was "too far afield in terms of establishing any type of potential defense" and to deny the motion without prejudice. After three fingerprints that were not Smith's were later found on the package's label, Smith could have renewed his motion. But, for reasons that are unclear, he chose not to do so. Smith also claims that he wanted to argue that it is illogical that only one print was found on the plastic bag. However, he could have called his expert to testify to this theory even without access to the bomb components and finger print exemplars; but he did not. The district court did not deny Smith access to a fingerprint expert, effectively or otherwise, nor did it deny him the opportunity to renew his motion when new finger-prints were discovered. Therefore, Smith has not shown that he was prejudiced by the district court's denial of his motion.

B. Admission of the Photograph

Smith next challenges the admission of a photograph taken by Bick that shows Smith making an obscene gesture. He asserts that the probative value of the photograph was low because it provided the jury no new information about Smith and Bick's relationship and that it was highly prejudicial because it could lead the jury to believe that Smith instigated the conflict between the two. He concludes that the district court should have kept the photograph from the jury.

A district court may exclude otherwise admissible evidence if its probative value is substantially outweighed by its prejudicial impact. Fed.R.Evid. 403; United States v. Chavis, 429 F.3d 662, 670 (7th Cir. 2005). But the district court has wide latitude in making this determination. See United States v. Strong, 485 F.3d 985, 991 (7th Cir. 2007). Because Smith objected at trial to the admission of the photograph, we review the district court's decision for abuse of discretion, see Chavis, 429 F.3d at 667, and will reverse only if no reasonable person could agree with the district court's conclusion. See United States v. Cash, 394 F.3d 560, 564 (7th Cir. 2005).

The district court's decision to admit the photograph was well within its discretion. The photograph was relevant because it demonstrated the nature of the relationship between Smith and Bick. It corroborated witness testimony that they were hostile towards each other and revealed that Smith might have had a motive to harm Bick. And the photograph was not unduly prejudicial to Smith because other evidence at trial showed that Smith and Bick had an acrimonious relationship. Government and defense witnesses testified that the two engaged in screaming matches, that Smith once punched Bick, and that Smith threatened to harm Bick "physically and financially." When viewed against the backdrop of the other evidence of animosity between Bick and Smith, the photograph did not reveal anything about Smith that the jury did not already know and therefore was not inflammatory. See United States v. Allen, 390 F.3d 944, 950 (7th Cir. 2004) (photograph depicting the defendant in police custody not unduly prejudicial because jury already knew defendant had been in custody). Furthermore, Smith had an opportunity to put the photograph into context for the jury, ameliorating any prejudicial effect. He testified that he was only responding to a similar gesture made by Bick. Thus, the photograph did not unfairly bias the jury against Smith.

C. Explosives Expert

Smith next challenges some of the testimony of the government's explosives expert. He concedes that the expert's conclusions were admissible under Federal Rule of Evidence 702, but argues that portions of the expert's presentation were unduly prejudicial and should have been disallowed. Specifically, Smith takes issue with the expert's use of a replica of the pipe bomb in a demonstration to show the jury how the bomb was intended to function. He argues that the expert's demonstration confused the jury by conflating a hypothetical pipe bomb with the actual pipe bomb and prejudiced the jury by giving undue weight to the government's theory that the bomb was intended to detonate.

Smith objected to portions of the expert's testimony at trial, so we review for abuse of discretion the court's decision to allow the testimony. See United States v. Davis, 471 F.3d 783, 788 (7th Cir. 2006).

The explosives expert first testified about how pipe bombs function generally and then described the components of the particular pipe bomb used. He expressed his opinion that the bomb was intended to explode and that an unintended glitch — likely a flaw in the electrical connection or a short in the igniter — caused it to malfunction. He described how he assembled a model of the bomb and then used the model to demonstrate how the actual bomb was intended to function. The demonstration caused a small flash, which showed how the bomb would have ignited. The judge made clear to the jury that the actual bomb did not explode — a fact that the jury had already heard many times during earlier testimony.

The district court properly allowed the expert's demonstration. The testimony was relevant because it was necessary to help the government meet its burden to prove that Smith attempted to use a bomb with intent to cause harm. See Chavis, 429 F.3d at 671. Evidence that is probative of an element of the offense should be admitted in all but the most egregious cases. See United States v. Kapp, 419 F.3d 666, 677 (7th Cir. 2005). The expert's testimony was important evidence that the bomb was designed to detonate and probative of the government's theory of the case. The government also was entitled to use its expert to counter Smith's theory that the bomb was designed specifically not to explode. See United States v. Glover, 479 F.3d 511, 518 (7th Cir. 2007).

And there was no undue prejudice to Smith. The expert's demonstration was not presented in an inflammatory way to incite the emotions of the jury. See Kapp, 419 F.3d at 677. And it is unlikely that the jury was confused, because it heard testimony that the actual bomb did not explode and the judge reminded the jury of this during the expert's testimony. See United States v. Kuzlik, 468 F.3d 972, 974-75 (7th Cir. 2006). The record also reveals that the demonstration involved a replica of the actual bomb, not, as Smith suggests in his brief, of a hypothetical pipe bomb, and we find no indication that the jury could have been confused. To be sure, the expert's testimony conflicted with Smith's defense theory that the bomb was not intended to explode, but Smith was free to cross-examine the expert, which he did, see Glover, 479 F.3d at 517, or to call his own expert.

The two cases cited by Smith are inapposite. In both, expert testimony was excluded because it was not in line with the proponent's theory of the case and was emotional and confusing to the jury. See Finchum v. Ford Motor Co., 57 F.3d 526, 530 (7th Cir. 1995) (demonstration showing car seat crash tests performed under conditions unlike those in actual accident); United States v. Gaskell, 985 F.2d 1056, 1061 (11th Cir. 1993) (demonstration involving shaking a doll was not similar to defendant's alleged actions). Here, by contrast, the expert's demonstration tracked the government's theory of the case — that the bomb was built to explode — and there is nothing to indicate that the demonstration incited the jurors' emotions or caused confusion.

D. Letter to Ishmael

Smith next argues that the district court should not have allowed the government to impeach him with a letter that he wrote to his friend Robert Ishmael, because, Smith contends, this letter is privileged under the work-product doctrine. The government argues that we cannot consider this argument on appeal because Smith waived his right to raise it by knowingly failing to object in the district court.

When a defendant fails to object to a district court's ruling, we generally say that he has forfeited the argument, and we will review the ruling for plain error. See United States v. Williams, 258 F.3d 669, 672 (7th Cir. 2001). However, when a defendant or his attorney makes a purposeful decision not to object, rather than carelessly or negligently failing to object, the defendant has waived his right to contest the issue on appeal, and we are precluded from reviewing the district court's decision. See United States v. Murry, 395 F.3d 712, 717 (7th Cir. 2005); United States v. Cooper, 243 F.3d 411, 416 (7th Cir. 2001). And an attorney who affirmatively states that he has no objection to admission of evidence waives the right to argue to the contrary. See United States v. Redditt, 381 F.3d 597, 602 (7th Cir. 2004).

Before trial, Smith's counsel described to the court in general terms the content of the letters Smith wrote to Ishmael and explained, "I've thought a lot about it, and I'm not sure that privilege attaches here." He then concluded, "I suppose that if Mr. Smith were to testify that we'd need to revisit this. But I don't plan on any kind of formal objection at this point." After opening statements, outside the hearing of the jury, Smith's counsel agreed with the government's attorney that "I don't see that there is a privilege either." When the letter was used to impeach Smith, defense counsel raised no objection. From defense counsel's comments, it appears that he considered whether to argue that the letter was privileged and made an affirmative decision not to do so. He did not carelessly or accidentally fail to raise an objection, rather, he intentionally chose to forego the argument. Thus, it has been waived, and we cannot revisit the district court's decision to allow the government to use the letter to impeach Smith.

However, even absent the waiver, allowing the use of the letter for impeachment purposes was proper because the letter is not privileged work product. The work-product privilege protects documents prepared by an attorney or the attorney's agent to analyze and prepare the client's case. See United States v. Nobles, 422 U.S. 225, 238-39, 95 S.Ct. 2160, 45 L.Ed.2d 141 (1975); Hobley v. Burge, 433 F.3d 946, 949 (7th Cir. 2006). It is not up to the client to determine whom to make an agent for the purposes of asserting the work-product privilege; the privilege extends to the work of the attorney's agents, not the client's agents. See Nobles, 422 U.S. at 238-39, 95 S.Ct. 2160. Though Ishmael is a private investigator and Smith wrote several letters to him detailing Smith's thoughts about his case and possible defense theories, Smith's counsel admitted to the district court that Ishmael was not involved in any investigation related to Smith's defense and had not been retained to do any work for the defense. The letters had nothing to do with Smith's legal representation and are not entitled to protection under the work-product doctrine.

E. Letter to Kehr

Smith also objects to the district court's decision to allow the government to impeach him with a letter that he wrote — but never sent — to Kehr. He argues that the government failed to disclose this letter in violation of Federal Rule of Criminal Procedure 16 and that the district court should have prohibited the government from using it at trial. Smith asserts that he was prejudiced by the use of the letter on cross-examination because, had he known about the letter earlier, his counsel would have asked him to explain it on direct examination, reducing its prejudicial impact. The government argues that its attorney maintained that he could not recall whether he turned the letter over to the defense at trial, and that, in any event, the district court's decision to allow it for impeachment purposes was not plainly erroneous.

Assuming that the letter was withheld, it is troubling that this document was not provided to the defendant until the government used it at trial in contravention of Rule 16 of the Federal Rules of Criminal Procedure, but it was not erroneous for the district court to allow it, because Smith was not prejudiced. See United States v. Warren, 454 F.3d 752, 760-61 (7th Cir. 2006). A Rule 16 violation prejudices a defendant only when he is unfairly surprised by the evidence and cannot adequately prepare his defense or when the violation has a substantial influence on the jury. See United States v. Stevens, 380 F.3d 1021, 1026 (7th Cir. 2004).

Smith testified on direct examination that he was no longer emotionally attached to Kehr when the bombing occurred. In the letter, dated May 12, 2003 — less than two months before the bombing — however, Smith indicated otherwise. Smith argues that he wrote but did not send the letter because his feelings towards Kehr changed, and that he should have had the opportunity to explain this on direct examination to minimize the impact of the letter. But his counsel had the opportunity to elicit this testimony on redirect and chose not to do so. And when defense counsel finally raised an objection to the use of the letter a month after trial, he admitted that at trial he thought that the letter was helpful to Smith's case. It is hard to see how the use of a piece of evidence that both the prosecution and defense believed supported their theories constitutes error. Furthermore, there was ample evidence besides the letter demonstrating that Smith had a motive to hurt Bick. Smith has not shown that the government's use of this letter prejudiced him.

F. Cumulative Effect of Errors

Smith next argues that the district court's cumulative errors denied him the right to a fair trial. Although any single error by itself may be insufficient to taint a jury, the combined effect of multiple erroneous rulings may result in significant harm necessitating another trial. See United States v. Santos, 201 F.3d 953, 965 (7th Cir. 2000). But this argument also fails. As we have described above, we can find no error in the district court's decisions. The court acted within its discretion, and Smith was not denied the right to a fair trial. See United States v. Banks, 405 F.3d 559, 570 (7th Cir. 2005).

III.

Finally, Smith contends that his mandatory consecutive 30-year sentence for carrying a pipe bomb while committing a crime of violence is unconstitutional because (1) it is cruel and unusual punishment prohibited under the Eighth Amendment and (2) it violates the Fifth Amendment prohibition on Double Jeopardy.

In support of his claim that his sentence violates the Eighth Amendment, Smith argues that the sentence is disproportionate to his crime. He contends that he received his sentence not because Congress determined it was appropriate, but because the prosecutor misused his discretion. Smith reasons that, because his crime injured no one, terrorism was not involved, and he does not have a history of violence, the prosecutor should not have charged him with a crime that carries such a severe penalty. He thus urges this court to act as a check on the prosecution's charging decisions.

We will uphold long prison sentences if the district court properly applied the relevant sentencing statute. See United States v. Arrington, 159 F.3d 1069, 1073 (7th Cir. 1998). Here, Congress has determined that a 30-year sentence is an appropriate penalty for violent crimes committed using explosives. See 18 U.S.C. § 924(c). The district court noted that, "what was proven here was an attempted murder in no uncertain terms." Bringing a pipe bomb to a place of business is a violent act and falls within the range of offenses that Congress intended to penalize severely, and the Eighth Amendment does not prohibit the 30-year mandated sentence. See Arrington, 159 F.3d at 1073; see also Harmelin v. Michigan, 501 U.S. 957, 994-95, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991) (life in prison for single drug crime not cruel and unusual punishment). So Smith's view that his sentence is disproportionate to his crime is incorrect.

Smith's argument that it was improper for the prosecutor to charge him with a crime that carries such a stiff penalty also lacks merit. Prosecutors always have discretion to decide which charges to bring, and this discretion extends to charges that carry enhanced statutory maximum penalties. See United States v. LaBonte, 520 U.S. 751, 762, 117 S.Ct. 1673, 137 L.Ed.2d 1001 (1997) (noting that prosecutorial discretion is an "appropriate" and "integral feature of the criminal justice system"). Further, the judiciary is not authorized to second-guess a prosecutor's decision to charge a particular crime unless the decision is made based on an invidious ground, which Smith does not claim here. See United States v. Roberson, 474 F.3d 432, 434 (7th Cir. 2007) (noting that it was improper for a district court judge to criticize the prosecutor's choice of charge).

Finally, Smith argues that his convictions under 18 U.S.C. § 844(i) and 18 U.S.C. § 924(c)(1)(A) punished him twice for the same conduct and thus violated the Fifth Amendment protection against Double Jeopardy. He acknowledges correctly that this argument has been rejected. A cumulative sentence does not run afoul of the Double Jeopardy Clause when at a single trial a defendant is convicted under two statutes and Congress has authorized cumulative sentences for violations of those statutes. See Missouri v. Hunter, 459 U.S. 359, 368-69, 103 S.Ct. 673, 74 L.Ed.2d 535 (1983); United States v. Handford, 39 F.3d 731, 733-34 (7th Cir. 1994). Smith concedes that he raises this issue only to preserve it for Supreme Court review, and it has been preserved.

IV.

For the above reasons, we AFFIRM the judgment of the district court.