In a game where you roll two fair six-sided dice, what is the probability of rolling a sum that is a prime number?

Instruction: Assume independent fair dice numbered 1–6. Calculate the probability that their sum is prime, accounting for the different numbers of ways to obtain each sum.

Context: This question assesses the candidate's ability to apply probability theory to dice games.

Updated

Official answer

For independent fair dice, the 36 ordered pairs are equally likely. The possible prime sums are 2, 3, 5, 7 and 11. Their respective numbers of ordered outcomes are 1, 2, 4, 6 and 2.

Therefore P(prime sum) = (1+2+4+6+2)/36 = 15/36 = 5/12, about 41.67%.

The sums are not uniformly distributed, so five prime sums out of eleven possible sums is not a valid probability calculation. One is not prime and is not a possible sum anyway.

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