Chapter 11.6, Problem 39HP

To determine

Find the probability that it is yellow, given that it is one of the sharpened pencils.

Answer to Problem 39HP

Option A is correct.

Explanation of Solution

Given:

A desk drawer contains 7 sharpened red pencils, 5 sharpened yellow pencils, 3 unsharpened red pencils, and 5 unsharpened yellow pencils. If a pencil is taken from the drawer at random, what is the probability that it is yellow, given that it is one of the sharpened pencils?

Options are: $\text{A:}\frac{5}{12};\text{B:}\frac{7}{20};\text{C:}\frac{5}{8};\text{D:}\frac{1}{5}$

Concept Used:

Favorable outcomes: {5 sharpened yellow pencil}

Possible outcomes: {7 sharpened red pencils, 5 sharpened yellow pencil}

Calculation:

Favorable outcomes: {5 sharpened yellow pencil}

Possible outcomes: {12 sharpened pencils}

Probability = $\frac{5}{12}$

Thus, Option A is correct.