suppose a pair of dice is rolled. Consider the sums of numbers on the top of the dice. Find the probabilities:

Question

a) P(5, given that the sum are odd)
b) P(odd, given that the sum rolled is 5)
c) P(7, given that one of the dice rolled was odd)

Answer 1

a) There are 36 possibilities. 18 of them are odd. Possible outcomes with a sum of 5 are: (1,4), (4,1), (2,3) and (3,2). The conitional probability is therefore 4/18 or 2/9.
b) If a sum of 5 is rolled, the sum is necessarily odd, so the conditional probability is 1.
c) The number of ways that only one die can be odd is:
(1,2), (1,4), (1,6), (3,2), (3,4), (3,6), (5,2), (5,4), (5,6), and the same combinations in reverse order, for a total of 18. Six of the combinations total 7, so the conditional probability is 6/18 = 1/3.