Question

A pet store has 13 puppies, including 4 poodles, 2 terriers and 2 retrievers if Rebecca and Aaron in that order each select one puppy at random replacement (they may both select the same one) find the probability that they both select a poodle

Answer 1

Explanation:

There are a total of 13 puppies in the store, including 4 poodles. Since Rebecca and Aaron are selecting with replacement, the probability of each selection is the same for both of them, and we can treat their selections as independent events.

The probability that Rebecca selects a poodle is 4/13, since there are 4 poodles out of 13 puppies.

The probability that Aaron also selects a poodle on his turn is also 4/13, since we are selecting with replacement and the probabilities are the same for each selection.

The probability of both events happening together (Rebecca and Aaron selecting a poodle) is the product of their individual probabilities:

P(both select a poodle) = P(Rebecca selects a poodle) * P(Aaron selects a poodle)

P(both select a poodle) = (4/13) * (4/13)

P(both select a poodle) = 16/169

Therefore, the probability that both Rebecca and Aaron select a poodle is 16/169.