Chapter 13, Problem 1E

To determine

To calculate: To find the probability that the shoes are either gray, white, size 11 or size 12

Answer to Problem 1E

The probability that the shoes are either gray, white, size 11 or size 12is $\frac{4}{5}$

Explanation of Solution

Given information: A store has gray, white or black shoes in sizes 8, 9, 10, 11 and 12 and a pair shoes is chosen at random

Formula Used:

Probability is defined as the likelihood of an event.

Probability is calculated as

  $\mathrm{Probability}=\frac{Event}{Outcomes}$

Calculation:

Event is defined as choosing a pair of shoes at random

Total number of possible outcomes $=3\times 5=15$

Possible outcomes shoes are either gray, white, size 11 or size 12

Color	Size
Grey	8, 9, 10, 11, 12
White	8, 9, 10, 11, 12
Black	8, 9, 10, 11, 12

Hence, number of possible outcomes $=12$

Thus, probability that the shoes are either gray, white, size 11 or size 12is calculated as

  $\begin{array}{l}P=\frac{12}{15}\\ P=\frac{4}{5}\end{array}$

Conclusion:

Hence, the required probability is $\frac{4}{5}$

Correct option is C