[TomCowley]

Yes, but it's not an interesting "no" answer. Assume there are 20 poker tournaments in a given town on a given day that finish at the same time. Exactly one of them has attendance in inverse proportion to IQ (lots of idiots, few geniuses). Somebody at this tournament flops back-to-back royal flushes. After the tournaments end, everybody is surveyed and asked "Do you believe somebody flopped back to back royals at tournament 1? Tournament 2? etc." Everybody not at the tournament will answer no to all with >95% confidence since it's a ridiculous longshot. Everybody at the tournament will answer yes (for their tournament) with 100% confidence since they saw it. Since this tournament is disproportionately dumb people, the number of people who say "no back-to-back royals" will increase with IQ, and they'll be wrong. Manipulate this tournament's IQ and attendance and you can come up with any survey results you want. This "counterexample" doesn't address the intent of the question.