A prime sum on prime dice

MediumProbability Combinatorics~5m

Two fair $6$ -sided dice have their faces labelled with the first six primes: $2, 3, 5, 7, 11, 13$ . Both are rolled. What is the probability that the sum of the two faces is itself prime?

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Odd + odd is even (not prime for sums $>2$ ); so a prime sum needs exactly one die to show the even prime $2$ .
Check $2+p$ for $p\in\{3,5,7,11,13\}$ : three work, each in $2$ ordered ways, over $36$ .

Answer

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0.1667 (± 0.001)

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Asked at: Jane Street, SIG

A prime sum on prime dice

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