An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots).

Question

Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 6. Event B: The sum is not divisible by 3 and not divisible by 6.

Answer 1

Here are the total possibilities for this:

Dice A: 1 2 3 4 5 6

D 1 2 3 4 5 6 7

I 2 3 4 5 6 7 8

C 3 4 5 6 7 8 9

E 4 5 6 7 8 9 10

5 6 7 8 9 10 11

B 6 7 8 9 10 11 12

You can see there are 21 cases where the sum is greater than 6 and there are a total of 36 possible cases. So the probability is 21/36 or 7/12.

For event B, I count 24 possibilities where the sum is not divisible by 3 or 6. So the probability is 24/36 or 2/3