A pair of dice is rolled. Find the probabilities of the given events

Question

A pair of dice is rolled. Find the probabilities of the given events. (Enter exact numbers as integers, fractions, or decimals.)

(a) The sum is 12.

(b) The sum is 12, given that the sum is even.

(c) The sum is 12, given that the sum is odd.

(d) The sum is even, given that the sum was 12

Answer 1

a) of 36 combinations which have sum equal to 12:

6 and 6

so probability is 1/36

b) if sum is 11, sum can't be 12, so probability is zero

c) if sum is 12, it cannot be odd, so probability is zero

d) if sum is 12 it will always be even, so probability is one.