One extra roll for more primes

MediumProbability~6m

Player 1 rolls a fair die $10000$ times; Player 2 rolls a fair die $10001$ times. A roll "scores" if it shows a prime ( $2$ , $3$ , or $5$ ). What is the probability that Player 2 scores strictly more primes than Player 1?

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A prime ( $2,3,5$ ) shows with probability $\tfrac36=\tfrac12$ - it's " $n{+}1$ vs $n$ fair coins."
By the standard symmetry argument for $p=\tfrac12$ , $\mathbb{P}[B>A]=\tfrac12$ exactly.

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0.5 (± 0.001)

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Asked at: Jane Street, Optiver

One extra roll for more primes

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