Question

Two number cubes are rolled for two separate events: a. All of the combinations of numbers on both cubes that give a sum less than 10. b. All combinations of numbers on both cubes that give a sumthat is a multiple of 3. In terms of a reduced fraction, find the conditional probability of B given that A occurs first.

Answer 1

All the possibilities of two numbers cubes are
11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
The probability that sum of the rolled cubes is less than 10 is
P = 6/36

The probability that the sum of the rolled cubes is a multiple of 3 is
P = 12/36

The conditional probability of B given that a occurs first is
P = 6/36 (12/36) = 1/18