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
9

.
Event
B

: The sum is an odd number.
Write your answers as exact fractions.

Answer 1

A die is a six-face solid and that rolling it twice will give us a sample space of 36 (calculated by multiplying 6 to itself).

(1) The outcomes that the sum of the two numbers will be greater than 9 are listed below:
5 and 5, 5 and 6, 6 and 5, and 6 and 6
There are four and the probability is equal to 4/36 or 1/9.

(2) The outcomes that the sum is an odd number is listed below:
1 and 2, 1 and 4, 1 and 6, 2 and 1, 2 and 3, 2 and 5, 3 and 2, 3 and 4, 3 and 6, 4 and 1, 4 and 3, 4 and 6, 5 and 2, 5 and 4, 5 and 6, 6 and 1, 6 and 3, 6 and 5
There are 18. Thus, the probability is 18/36 or 1/2.