NYGAARD, Circuit Judge.
Raymond Isaac was charged with: (1) conspiracy to possess marijuana with intent to distribute, in violation of 21 U.S.C. § 846; (2) possession of marijuana with intent to distribute, in violation of 21 U.S.C. § 841(a)(1); and (3) possession of marijuana on board a vessel arriving in the United States, in violation of 21 U.S.C. § 955. The jury found him guilty on the first two counts, and not guilty on the third. Isaac appeals his convictions, claiming that the district court inaccurately described the reasonable-doubt standard for the jury; failed to caution the jury on assessing the credibility of witnesses who, according to Isaac, should be considered accomplices or immunized witnesses; neglected to take judicial notice of the fact that identical charges against those witnesses were dropped "in response to the government's motion to dismiss" and allowed the prosecutor to intimate that Isaac's decision not to testify was evidence against him. We will affirm.
I. FACTS
On August 5,1994, a boat mechanic working near docks used by the St. Thomas police marine unit noticed a strange boat tied up beside an abandoned barge and called Corporal Alan Roberts of the marine unit. When Corporal Roberts arrived, he found two men sitting on the barge, dressed in shorts and short-sleeved shirts and barefoot. They looked tired, bruised, sunburnt and dehydrated. Upon questioning by Corporal Roberts and U.S. Customs agents, the men identified themselves as Conrad Brown and Irvin Reid and said that they had arrived on the boat from Jamaica. They also described a man they knew as "Rocky," who, they said, had accompanied them from Jamaica and had left the boat when they docked.
Later, Roberts and U.S. Customs Agent Willis Smiley saw a man fitting the description of "Rocky" get out of a van that had pulled up near the dock. When Corporal Roberts and Agent Smiley [472]*472approached the man, the van and an accompanying car sped off, but the man made no attempt to leave. Asked his name, the man replied, "Rocky." Agent Smiley then asked him what his real name was and he replied, "Raymond Isaac." Isaac was shown to Brown and Reid, and they identified him as the "Rocky" who had arrived with them in the boat from Jamaica. When customs agents searched the boat they found 29 bales of marijuana weighing approximately 582 pounds.
Isaac, Brown and Reid were charged with conspiracy to possess marijuana with intent to distribute, possession of marijuana with intent to distribute, and possession of marijuana on board a vessel arriving in the United States. On the day the trial was to begin, the government moved to dismiss the charges against Brown and Reid. In a simultaneous motion to designate Brown and Reid as material witnesses and detain them pending Isaac's trial, the government stated that the charges against Brown and Reid had been dropped "in the interest of justice and the witnesses['] cooperation."
At Isaac's subsequent trial, Brown and Reid testified that they had set out on July 31, 1994 to go fishing with "Rocky." Because it was a windy day, they had taken a larger, community-owned vessel called the "Community Aid." Brown and Reid were dressed for a day offishing, barefoot, in shorts and short-sleeved shirts. The three of them first stopped in Port Royal, where Isaac disembarked to get beer. He returned with a friend, and asked that the friend be allowed to accompany them. Brown agreed, and they fished for several hours. Isaac and his friend then had Brown and Reid take them to a nearby deserted island named Lime Cay. While Isaac and his friend drank beer under a tree, Brown and Reid took a walk. When they returned, Isaac asked Brown if he would like to do "a drug move" for $20,000 in Jamaican dollars. Brown initially agreed, but then changed his mind when he grasped that a lengthy trip was involved. At that point, Brown and Reid claimed that Isaac's friend threatened them with a gun and forced them to remain on Lime Cay while he and Isaac departed in the boat. Brown was ready to swim to the mainland, but Reid did not think he could swim the nine or ten mile distance, so the two of them remained on the island.
[473]*473Several hours later, Isaac and his friend returned. The two five-gallon canisters of gasoline with which the boat had been equipped were gone, replaced by seven fifty-five-gallon drums of gasoline. The bow, which had been open, was now covered with a piece of plywood. Isaac's friend forced Brown and Reid to board at gunpoint, and Isaac, Brown and Reid departed, leaving the friend behind on the deserted island.
Brown and Reid testified that they sailed for days, while Isaac navigated with the aid of charts and a global positioning system. Although Brown was at the helm most of the time, Isaac took over when they neared St. Thomas, and piloted the boat to the dock where it was discovered. Upon docking, Isaac left, telling Brown and Reid he would return. Shortly thereafter Brown and Reid were found and arrested.
Brown testified that early in the trip he had planned to jump overboard and swim to safety, but he was dissuaded by Reid, who could not swim well. Neither made any further attempt to escape: they had never been far from Jamaica and did not know how to read the charts or use the global positioning system; moreover, until arrested, they did not encounter anyone whom they could ask for help.
II. JURY INSTRUCTION ON REASONABLE DOUBT
The district court instructed the jury that it could convict Isaac only if the government had proven him guilty beyond a reasonable doubt, explaining the evidentiary standard as follows:
Reasonable doubt is a term often used, probably well understood, but not easily defined. Reasonable doubt is what the term implies. The doubt must be reasonable. It is not a mere possible or imaginary doubt, because as you well know, everything relating to human affairs, and depending on oral testimony, is open to some possible or imaginary doubt. The government is not required to produce evidence that will exclude every possibility of a defendant's innocence. It is only required to prove his guilt beyond a reasonable doubt, not beyond all possible doubt. The test is one of reasonable doubt. A reasonable doubt is a fair doubt, based upon reason and common [474]*474sense — the kind of doubt that would make a reasonable person hesitate to act. Proof beyond a reasonable doubt must, therefore, be proof of such a convincing character that you would be willing to rely and act upon it, unhesitatingly, in the most important of your own affairs.
While bearing in mind that it is rarely possible to prove anything to an absolute certainty, you must remember, as well, that a defendant must never be convicted on mere assumption, conjecture or speculation. So if the jury views the evidence in the case as reasonably permitting either of two conclusions, one of innocence, the other of guilt, the jury should, of course, adopt the conclusion of innocence.
Reasonable doubt may arise also from a lack of evidence or proof. If you find that the government has failed to produce evidence sufficient to satisfy you of the guilt of the defendant beyond a reasonable doubt, then he is entitled to an acquittal, or a verdict of "not guilty." But if, after considering all of the evidence and giving the accused the benefit of a reasonable doubt, both as to the evidence presented or the lack of evidence, you are led to the conclusion that he is guilty, you should so declare by your verdict.
Isaac points to several aspects of this charge which, he contends, misled the jury by suggesting that an improperly low level of certainty was required for conviction, in violation of the Fifth and Sixth Amendments.
The Constitution requires that the government prove every element of criminal charge beyond a reasonable doubt to obtain a conviction. In re Winship, 397 U.S. 358, 364, 90 S. Ct. 1068, 1073 (1970). While a trial court must advise the jury of the government's burden of proof, no particular set of words is mandated. Victor v. Nebraska, 511 U.S. 1, 5, 114 S. Ct. 1239, 1243 (1994). Due process is satisfied if the instructions, taken as a whole, accurately convey the concept of reasonable doubt to the jury Id. (citing Holland v. United States, 348 U.S. 121, 140, 75 S. Ct. 127, 137 (1954)). Thus, although we have considered each of Isaac's criticisms, ultimately we must [475]*475determine whether the entire instruction the jury received led it to apply the correct standard of proof. If not, Isaac's conviction will be reversed. Sullivan v. Louisiana, 508 U.S. 275, 279-80, 113 S. Ct. 2078, 2081-82 (1993).
Isaac levels his most cogent criticism at the portion of the district court's instruction that directed the jury to find him not guilty if the evidence supported two inferences, one of guilt, the other of innocence. The Second Circuit Court of Appeals has held that the "two-inference" instruction is improper because it "may mislead a jury into thinking that the government's burden is somehow less than proof beyond a reasonable doubt." United States v. Inserra, 34 F.3d 83, 91 (2d Cir. 1994) (quoting United States v. Khan, 821 F.2d 90, 93 (2d Cir. 1987)). In a decision issued three weeks after Isaac's trial, we urged trial courts to heed the Second Circuit's criticism of the "two-inference" instruction when it is specifically brought to their attention. United States v. Jacobs, 44 F.3d 1219, 1226 & n.9 (3d Cir.), cert. denied, 115 S. Ct. 1835 (1995). Isaac's counsel did make a timely objection to this instruction, citing Khan.
Although we disapproved of the "two-inference" instruction in Jacobs, we did not hold that the instruction was so constitutionally deficient per se that it infected the entire instruction on reasonable doubt. 44 F.3d at 1226. Accordingly, we will consider whether this deficiency was rectified by the remainder of the reasonable doubt instruction.
Isaac argues that so much of the charge was phrased in terms of what reasonable doubt is not, that it only served to confuse and mislead the jury. We disagree. The practice of defining reasonable doubt by what it is not is well established. For instance, the definition formulated by Justice Shaw of the Massachusetts Supreme Judicial Court more than a century ago, which has served as a model instruction, begins by explaining that reasonable doubt "is not mere possible doubt . . . ." Victor, 511 U.S. at 8, 114 S. Ct. at 1244 (quoting Commonwealth v. Webster, 59 Mass. 295, 320 (1850)). More recently, the U.S. Supreme Court has affirmed judgments in two cases where the trial court explained reasonable doubt by contrasting what it is with what it is not. 511 U.S. at 7, 18, 114 S. Ct. at 1244, 1249.
Here, the court contrasted reasonable doubt with "all possible doubt" and "imaginary doubt," and explained that, while it was [476]*476not "absolute certainty/' neither was it "mere conjecture or speculation." The court also stated the reasonable doubt was "a fair doubt" of the sort that would make a person hesitate to act. We are satisfied that the court made appropriate use of the negative examples, which were contrasted with positive examples to create a.framework for the jury's understanding.
Finally, Isaac objects to the court's explanation that proof beyond a reasonable doubt is "proof of such a convincing character that you would be willing to rely and act upon it, unhesitatingly, in the most important of your affairs." Isaac argues that this language was disapproved by the Supreme Court in Holland. We read the case differently. In Holland, the Court recommended that the reasonable doubt section of the jury charge be phrased "in terms of the kind of doubt that would make a person hesitate to act" rather than "the kind of doubt. . . which you folks in the more serious and important affairs of your own lives might be willing to act upon." 348 U.S. at 140, 75 S. Ct. at 138. We find that the instructions the court gave in this case properly heeded the Supreme Court's recommendation by stressing the need for convincing proof, and using the word "unhesitatingly." Moreover, in the preceding sentence of the charge, the court quoted the Holland formulation almost verbatim, stating that reasonable doubt is "the kind of doubt that would make a reasonable person hesitate to act."
As a whole, the court's instructions adequately conveyed the government's burden of proof to the jury. The court repeatedly stated that the government was required to prove its case beyond a reasonable doubt, and that the burden never shifted to the defendant. The court accurately explained that the standard was high, but not to the point of absolute certainty or to the exclusion of possibilities which defy common sense. By analogizing the standard of proof to the level of certainty an individual would require before unhesitatingly acting in important personal affairs, the court provided jurors with a comprehensible benchmark. Although the use of the "two-inference" example suggested that the standard is lower than it is, this defect was counterbalanced by the explanation that preceded and succeeded it. Accordingly, we conclude that the jury instruction, taken as a whole, was not constitutionally deficient.
[477]*477III. JURY INSTRUCTION ON WITNESS CREDIBILITY
Isaac contends the district court violated his Fifth Amendment right to due process and a fair trial, and his Sixth Amendment right to confrontation, by denying his request that the jury be instructed to weigh the testimony of Brown and Reid with greater care because they were immunized witnesses and accomplices.1 Although it would have been better had the district court given the instruction, we conclude that this jury was sufficiently apprized of the credibility concerns posed by the testimony of immunized witnesses Brown and Reid.
We recognize that a witness who has been given a reward for cooperation has also been given an incentive to shade the truth or to lie. It may well be the better practice to give an instruction if requested. However, such an instruction is not required, especially when, as here, it has been made clear to the jury that it is permitted to disbelieve testimony to the extent it finds that the testimony was driven more by a self-serving desire for leniency than a sense of duty to tell the truth. We have repeatedly approved the practice of counseling jurors to view the testimony of accomplices and immunized witnesses with skepticism and caution, particularly when it is uncorroborated and material to establishing the defendant's guilt. See, e.g., United States v. Rosa, 560 F.2d 149, 156 (3d Cir. 1977); United States v. Bromwell, 467 F.2d 895, 896 (3d Cir. 1972); United States v. Schanerman, 150 F.2d 941, 943 (3d Cir. 1945); Marsh v. United States, 82 F.2d 703, 704 (3d Cir. 1936). Nevertheless, to date we have not determined whether it is error per se for a trial court to refuse to give such an instruction even when, as here, it was requested. Cf. United States v. Wright, 921 F.2d 42 (3d Cir. 1990) (considering whether it was plain error for court not to give an informant charge when defense counsel failed to make a timely request). We decline to do so now.
It has long been recognized that testimony of accomplices and informers raises particular credibility problems since these witnesses have strong incentives to fabricate or mold their testimony [478]*478as the government desires in order to escape prosecution, lighten their sentences, obtain remuneration or receive protection. See Cool v. United States, 409 U.S. 100, 103, 93 S. Ct. 354, 357 (1972); On Lee v. United States, 343 U.S. 747, 757, 72 S. Ct. 967, 973- 74 (1952). Consequently, the defendant is entitled to broad latitude in probing the credibility of such witnesses by cross-examination, and to have the jury properly instructed. See Hoffa v. United States, 385 U.S. 293, 311- 12, 87 S. Ct. 408, 418-19 (1966). Although no particular instruction is mandated, warning the jury to consider the testimony of an accomplice with great care and caution before relying on it is appropriate. Marsh, 82 F.2d at 704 (citing Caminetti v. United States, 242 U.S. 470, 495, 37 S. Ct. 192, 198 (1916); Crawford v. United States, 212 U.S. 183, 203-04, 29 S. Ct. 260, 268 (1908).
Courts were initially admonished to give cautionary instructions at a time when juries were counseled that witnesses are presumed to speak the truth. See Crawford, 212 U.S. at 204, 29 S. Ct. at 268. We have held, however, that a defendant's right to the presumption of innocence is violated if a jury is instructed that witnesses are presumed to speak the truth. United States v. Johnson, 371 F.2d 800, 804-05 (3d Cir. 1967); accord United States v. Evans, 398 F.2d 159, 162 (3d Cir. 1968). Juries are now advised that they are the judges of all witnesses' credibility. For instance, here the trial court said:
You can determine the truth by resolving the degree of credibility or reliability of the witnesses who have been produced before you. You are to decide the factual situation by carefully scrutinizing and analyzing the testimony of each and every witness, with a view toward determining whether a witness is neutral or friendly, or whether the witness has told the truth or exaggerated his testimony.
In this situation, the necessity for an immunized witness or accomplice instruction is reduced. Therefore, we prefer to allow the trial court the discretion to decide whether to include an immunized witness or accomplice instruction in the charge to the jury. See United States v. Smith, 789 F.2d 196, 204 (3d Cir. 1986) (noting the trial court has wide discretion in charging the jury); see also United States v. Cook, 102 F.3d 249, 252 (7th Cir. 1996) (commit[479]*479ting the decision to give an instruction on the credibility of informer testimony to the discretion of the trial court). The trial court will generally be acting within its discretion if it allows defense counsel broad latitude to probe the credibility of accomplices and immunized witnesses, and instructs the jury to consider whether the witnesses' self-serving motives in testifying have destroyed or diminished their credibility. An immunized witness or accomplice charge is advisable when the jury has not otherwise been sufficiently alerted to the credibility concerns posed by the testimony of witnesses over whom the government wields particular power to reward or punish. See Cook, 102 F.3d at 252.
We conclude that the trial court did not abuse its discretion by refusing to give a specific accomplice or immunized witness charge. First, Isaac's attorney was permitted to conduct a vigorous defense. He repeatedly pointed out in cross-examination and argument to the jury that the government had no direct evidence, beyond the testimony of Reid and Brown, that Isaac had ever been on board the Community Aid or had forced Reid and Brown to accompany him from Jamaica. Isaac's attorney also brought out the facts that Reid and Brown had initially been indicted on the same charges as Isaac, and that they were represented by private counsel whose fees were being paid by an unknown source. Moreover, the cross-examination of Reid and Brown revealed that, although the charges against them had been dropped, they were still being kept in prison as material witnesses and realized they would not be freed until they had testified against Isaac. Thus, Isaac's counsel brought to the jury's attention factors which suggested that Reid and Brown might be motivated to give false evidence and that, without this suspect testimony, evidence of Isaac's involvement in the smuggling operation was slim.
Second, the trial court instructed the jury that they were the judges of credibility and should consider the witnesses' motives, the circumstances under which they had testified and the relationship each might have to the prosecution or the defense. The court's instructions, taken together with defense counsel's vigorous attack on the credibility of Reid and Brown, certainly put the jury on notice that it had to weigh carefully the possible accomplices' testimony. See Hoffa, 385 U.S. at 311-12 & nn.12-14, 87 S. Ct. at [480]*480418-19 & nn.12-14 (holding that no violation of the Due Process Clause occurred where the informer was rigorously cross- examined and the trial court both recapped the defendant's version of events for the jury and gave it a general instruction on assessing witness credibility). The fact that the jury acquitted Isaac of possessing marijuana on board a vessel arriving in the United States indicates that the jury took these instructions seriously, since Reid's and Brown's testimony, if credited, would have been sufficient to convict Isaac on this count as well.
IV. JUDICIAL NOTICE OF DISMISSAL OF CHARGES AGAINST REID AND BROWN
Isaac argues that his Fifth Amendment right to due process was violated when the court took judicial notice that all charges against Reid and Brown were dismissed, but did not add that this was done "in response to the government's motion." Isaac contends that the omission "placed a judicial imprimatur and enhancement on the credibility of Brown and Reid" by implying that the court had independently dismissed the charges, presumably for lack of evidence.
Rule 201 of the Federal Rules of Evidence requires the court to take judicial notice of facts "capable of accurate and ready determination by resort to sources whose accuracy cannot reasonably be questioned" when a party requests that it do so and supplies the necessary information. Fed. R. Evid. 201(b), (d). In this instance, the fact that the charges against Reid and Brown had been dropped on the motion of the United States was readily ascertainable from the court order, entered into evidence at Isaac's trial as Exhibit F. Indeed, when the court ruled on the defendant's motion to take judicial notice of certain facts, the court agreed to include the words "in response to the government's motion"; their omission from the judicially noticed facts read to the jury seems to have been inadvertent, not deliberate.
Nonetheless, the judicial order dismissing the charges against Brown and Reid was entered into evidence, and it clearly stated that the charges were dismissed on the motion of the government. In addition, the government's motion to designate Reid and Brown as material witnesses was also entered into [481]*481evidence; the supporting affidavit stated that the drug charges had been dismissed "in the interest of justice and the witnesses!'] cooperation," a point defense counsel drove home in his closing argument. Consequently, the jury was not misled into believing that the court had independently dismissed the charges against Brown and Reid.
V. PROSECUTOR’S CLOSING ARGUMENT
Finally, Isaac argues that his Fifth Amendment right not to testify was violated when the prosecutor stated, over defense counsel's objection, "Raymond Isaac captained that boat from Jamaica, and the only people who would know that Raymond Isaac captained that boat from Jamaica are Raymond Isaac, Conrad Brown, Irvin Reid, and that fourth individual in Jamaica. Those are the only people." According to Isaac, the prosecutor was implying that Isaac's decision not to testify and give his version of what did or did not happen on the boat was evidence of his guilt.
In Griffin v. State of California, the Supreme Court held that the Fifth Amendment prohibits the judge and prosecutor from suggesting to the jury that it may treat the accused's silence as substantive evidence of guilt. 350 U.S. 609, 615, 85 S. Ct. 1229, 1233 (1965); see also Baxter v. Palmigiano, 425 U.S. 308, 319, 96 S. Ct. 1551, 1558 (1976). Otherwise, the defendant is penalized by the court for exercising his constitutional right not to incriminate himself. Griffin, 350 U.S. at 614, 85 S. Ct. at 1232-33. However, when the defendant uses his Griffin protection as a sword, rather than a shield, the prosecution may respond appropriately. See United States v. Robinson, 485 U.S. 25, 32, 108 S. Ct. 864, 869 (1988). For instance, in Robinson, the Supreme Court held that once defense counsel had asserted in closing argument that the government did not allow the defendant to tell his side of the story, it was not a violation of the Fifth Amendment for the prosecutor to respond by telling the jury that the defendant could have testified if he so chose. Id. at 26-28 & n.2, 108 S. Ct. at 866 & n.2. Thus, we must consider the prosecutor's remarks in context to determine whether they are a fair response to an assertion by the defendant. Id. at 32-33, 108 S. Ct. at 869.
[482]*482When the prosecutor's statement here is considered in context, we find that, although it comes close to violating Griffin, it was a fair response to defense counsel's closing argument. Much of that argument was an attack on the credibility of Brown and Reid, whose testimony was key to proving numerous elements of the government's case. The prosecutor began his rebuttal by conceding that Brown and Reid were probably not the most upstanding individuals; however, there were no paragons of virtue present during the smuggling operation who could testify about it. In this context, the prosecutor's declaration that "the only people who would know that Raymond Isaac captained the boat are Raymond Isaac, Conrad Brown, Irvin Reid, and that fourth individual in Jamaica" comes across as an assertion that the government obtained its evidence from the only available sources. Although the prosecutor would probably have been better advised, given Griffin, to omit the reference to Isaac, the comment was not "of such character that the jury would naturally and necessarily take it to be a comment on the failure of the accused to testify." United States v. Chaney, 446 F.2d 571, 576 (3d Cir. 1971).
VI. CONCLUSION
Because we conclude that Isaac's rights under the Fifth and Sixth Amendments were not violated, his convictions on the counts of conspiracy to possess a controlled substance with intent to distribute in violation of 21 U.S.C. § 846 and possession of a controlled substance with intent to distribute in violation of 21 U.S.C. S 841(a)(1) will be affirmed.