Question

Find the conditional​ probability, in a single roll of two fair​ 6-sided dice, that the sum is less than 6​, given that the sum is odd.

Answer 1

Sum (x)	P(x)
2	1/36
3	2/36
4	3/36
5	4/36
6	5/36
7	6/36
8	5/36
9	4/36
10	3/36
11	2/36
12	1/36

P[ sum is less than 6​, given that the sum is odd ] = P[ sum is less than 6 and the sum is odd ] / P[ the sum is odd ]

P[ sum is less than 6 and the sum is odd ] = Number of times sum is less than 6 and the sum is odd / total number of cases

P[ sum is less than 6 and the sum is odd ] = 2/36

P[ the sum is odd ] = Number of times the sum is odd / total number of cases

P[ the sum is odd ] = 5/36

P[ sum is less than 6​, given that the sum is odd ] = (2/36)/(5/36)

P[ sum is less than 6​, given that the sum is odd ] = 2/5

P[ sum is less than 6​, given that the sum is odd ] = 0.4