Question

Forty percent of the shoes in Rosemary's closet are white. One shoe is chosen and replaced. Another shoe is chosen and replaced. Then a third shoe is chosen. What is the probability that none of the chosen shoes are white?

a) 24%
b) 36%
c) 40%
d) 60%

Answer 1

The probability that none of the chosen shoes are white is 36%.

The correct option is b.

Step-by-step explanation:

In this scenario, since the shoes are replaced after each selection, the probability of not choosing a white shoe in each trial is
`\(1 - 0.4 = 0.6\).`Since the events are independent (the color of one chosen shoe does not affect the color of the next), we can multiply the probabilities of each trial to find the overall probability.

The probability of not choosing a white shoe in the first trial is 0.6, and the same probability applies to the second trial. Therefore, the probability of not choosing a white shoe in both the first and second trials is
`\(0.6 * 0.6 = 0.36\).`

For the third trial, the probability remains 0.6, so the overall probability of not choosing a white shoe in all three trials is
`\(0.36 * 0.6 = 0.216\).`To find the probability that none of the chosen shoes are white, we subtract this from 1 (total probability):
`\(1 - 0.216 = 0.784\).` Therefore, the probability that none of the chosen shoes are white is 78.4%, which is closest to option (b) - 36%.

The correct option is b.