Two six-sided dice were rolled

Question

Two six-sided dice were rolled, and a friend tells us that the numbers that came up were identical. Find the probability that the sum of the numbers was as follows. (Enter your probabilities as fractions.)

(a) 2

(b) 11

(c) an even number

(d) an odd number

Answer 1

(a) The only way we could have a sum of two is if we rolled a 1 and a 1

P(sum is 2) = 1/6 * 1/6 = 1/36

(b) We could only have a sum of 11 if we rolled a 5,6 and those numbers aren't identical

P(sum is 11) = 0/6 = 0

(c) We could have an even sum with identical numbers with the following rolls: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

P(sum is even) = (1/6 * 1/6) + ... + (1/6 * 1/6)

P(sum is even) = 6 (1/6 * 1/6) = 6 * 1/36 = 1/6

(d) If the two numbers are identical, we could not have an odd sum

P(sum is odd) = 0/6 = 0