Wu rolls two fair, six-sided dice. You are not told what the rolls were, but you are told that the sum of the two rolls is a prime. What is the probability that the sum of the rolls is 3?
On a roll of 2 dice, there are 15 ways of getting a prime number. But, there are only 2 ways of getting the sum of 3, and that is: 1+ 2 and 2+1:
Therefore, the probability is: 2 / 15
(1, 1) , (1, 2) , (1, 3) , (1, 4) , (1, 5) , (1, 6) , (2, 1) , (2, 2) , (2, 3) , (2, 4) , (2, 5) , (2, 6) , (3, 1) , (3, 2) , (3, 3) , (3, 4) , (3, 5) , (3, 6) , (4, 1) , (4, 2) , (4, 3) , (4, 4) , (4, 5) , (4, 6) , (5, 1) , (5, 2) , (5, 3) , (5, 4) , (5, 5) , (5, 6) , (6, 1) , (6, 2) , (6, 3) , (6, 4) , (6, 5) , (6, 6) , Total == 36
