Three primes in six rolls

A fair 66-sided die is rolled 66 times. A roll is a "success" if it shows a prime number. What is the probability of exactly 33 successes?

Show hints (2)+
  1. Which die faces are prime? That fixes the per-roll success probability.
  2. It's (63)p3(1p)3\binom{6}{3}p^3(1-p)^3 with p=1/2p=1/2.

Answer

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0.3125

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Asked at: Optiver, Akuna Capital

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