Question

a pet store has 13 puppies, including 4 poodles, 4 terriers, and 5 retrievers. if rebecca 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
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Calculate the probability of Rebecca selecting a poodle

The probability of Rebecca selecting a poodle is the number of poodles divided by the total number of puppies. There are 4 poodles and 13 puppies in total. So the probability \(P(\text{Rebecca poodle})=\frac{4}{13}\).

Step2: Calculate the probability of Aaron selecting a poodle

Since the puppy is replaced, the situation for Aaron is the same as for Rebecca. The probability \(P(\text{Aaron poodle})=\frac{4}{13}\).

Step3: Calculate the probability that both select a poodle

For independent events (the selection of Rebecca and Aaron are independent because of replacement), the probability that both events occur is the product of their individual probabilities. So \(P(\text{both poodles}) = P(\text{Rebecca poodle})\times P(\text{Aaron poodle})\).
Substitute the values: \(P(\text{both poodles})=\frac{4}{13}\times\frac{4}{13}=\frac{16}{169}\approx 0.095\)

Answer:

\(0.095\)