Question

A pet store has 10 puppies, including 2 poodles, 5 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.
The probability is ___

Answer 1

$P = 1/25 or P = 0.04$

This is an example of probability problem with replacement. The pet store has 10 puppies so the sample size is 10. The event size is depending on the number of puppies in each breed. Therefore, the event size is 2 for poodles, 3 for retrievers and 5 for terriers. Rebecka chooses a puppy at random and the probability that it is a poodle is 2/10 or 1/5. Since the store replaces the chosen puppy with the puppy of the same breed, the remaining sample size is still 10 and the event size is still the same. Therefore, the probability that Aaron chooses a poodle is still 2/10 or 1/5. For two dependent events, their probabilities are multiplied. Therefore, the probability that both select a poodle is 1/25.