Find the probability that they both select a poodle.

Question

A pet store has 11 puppies, including 5 poodles, 3 terriers, and 3 retrievers. If Rebecka selects one puppy at random, the pet store replaces the puppy with a puppy of the same breed, then Aaron chooses a puppy at random. Find the probability that they both select a poodle.

Answer 1

11 puppies = 5 poodles + 3 terriers + 3 retrievers

P(Rebecka selects a poodle) = 5/11

P(Aaron selects a poodle) = 5/11

P(both select a poodle) = (5/11)*(5/11) = 25/121 ≈ 0.2066

The probability of both Rebecka and Aaron select a poodle is about 0.2066. Keep in mind that these events are independent because the first event didn't affect the second event. In terms of replacement, the first time the poodle was selected the store replaced with the same breed of the puppy for the next customer to come choose their puppy. The sample size will not be affected in future events.