Question

1/5 of the shoes in a factory are green. If you pick a shoe, replace it, pick another shoe and replace it, and pick a third shoe, what is the probability that none of the shoes are green?

Answer 1

The probability that none of the three shoes selected are green = 64/125

Explanation:

If we have 1/5 of shoes being green, then the number of non-green shoes = 1-1/5 = 4/5

Now, this is a probability with replacement.

probability of the first shoe since it’s not green = 4/5

probability of second shoes since it’s not green = 4/5

probability of third shoe since it’s not green = 4/5

Now, the probability that none of the shoes are green = 4/5 * 4/5 * 4/5 = 64/125