An ordinary (fair) die is a cube with the numbers ...

Question

An ordinary (fair) die is a cube with the numbers 1

 through 6

 on the sides (represented by painted spots). 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 5

.

Event B

: The sum is an even number.

Write your answers as fractions.

Answer 1

11 possible outcomes

sums of

2,3,4,5,6,7, 8, 9, 10, 11, 12

only 1 way to get 2, 1 and 1

2 ways to get 3, 1 and 2, or 2 and 1

3 ways to get 4, 1 and 3, 3 and 1 or 2 and 2

4 ways to get 5

5 ways to get 6

6 ways to get 7

5 ways to get 8

4 ways to get 9

3 ways to get 10

2 ways to get 11

1 way to get 12

that sums up to 36 different ways to get 2 through 12

4+3+2+1 =10 ways to get 5 or less out of 36

Pr(5 or less)= 10/36 = 5/18

Pr(more than 5) = 1-5/18 = 13/18

Pr(even outcome) = 1+3+5+5+3+1 all over 36 = 18/36 = 1/2

that's the ways to get 2,4,6,8,10 or 12 over 36