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