Question

Kelly rolls two number cubes. Determine the probability of each of the following events.

Express each probability as a fraction in simplest form.

A. The sum of the number cubes is 7.

B. The sum of the number cubes is less than 4.

Answer 1

(a)1/6

(b)1/12

Explanation:

Given that the cubes are numbered from 1 to 6.

The possible outcomes are:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Total number of possible Outcomes=36

Part A

Probability that the sum of the number cubes is 7.

The outcomes that sums up to 7 are:

(1,6) (2,5) (3,4) (4,3) (5,2) (6,1)

Number of outcomes=6

Therefore:

P(sum of the number cubes is 7)=6/36=1/6

Part B

The sum of the number cubes is less than 4.

Outcomes in which the sum is less than 4 are:

(1,1) (1,2) (2,1)

Number of outcomes=3

Therefore:

P(sum of the number cubes is less than 4)=3/36=1/12