Vaibhavgarg999
In a certain game, a player rolls three fair six-sided dice. Each die shows a number from 1 to 6. Let AA be the event that the sum of the numbers on the dice is exactly 9. Let BB be the event that the sum of the numbers on the dice is a multiple of 3. What is the probability that AA occurs given that BB has occurred?
25/72.
3 - 1,1,1 = (1)
6 - 3,2,1; 3,1,2; 2,1,3; 2,3,1; 1,3,2; 1,2,3; 4,1,1; 1,4,1; 1,1,4; 2,2,2 = {6+3+1} = (10)
Similarly,
9 - 6,2,1; 5,3,1; 4,3,2; 2,2,5; 1,4,4; 3,3,3 = {6+6+6+3+3+1} = (25) OR AA
12 - 6,4,2; 6,3,3; 5,5,2; 5,4,3; 6,5,1; 4,4,4 = {6+3+3+6+6+1} = (25)
15 - 6,6,3; 6,5,4; 5,5,5 = {3+6+1} = (10)
18 - 6,6,6 = (1)
BB = 1 + 10 + 25 + 25 + 10 + 1 = 72
[b]AA/ BB = 25/72. [\b]