Questions: A pet store has 9 puppies, including 5 poodles, 3 terriers, and 1 retriever. Rebecka and Aaron, in that order, each select one puppy at random without replacement. Find the probability that Aaron selects a retriever, given Rebecka selects a retriever. The probability is (Type an integer or a simplified fraction.)

Solution Steps

The main idea is to recognize that the event of interest cannot occur because once the only retriever is selected by the first person, it is no longer available for the second person to select. This is an example of conditional probability where the condition makes the event impossible.

The total number of puppies in the pet store is given as \( 9 \).

There is \( 1 \) retriever among the \( 9 \) puppies.

The probability that Rebecka selects the retriever is calculated as follows: \[ P(\text{Rebecka selects retriever}) = \frac{\text{Number of retrievers}}{\text{Total number of puppies}} = \frac{1}{9} \approx 0.1111 \]

If Rebecka selects the retriever, there are no retrievers left for Aaron to select. Therefore, the probability that Aaron selects a retriever given that Rebecka has already selected the retriever is: \[ P(\text{Aaron selects retriever} \mid \text{Rebecka selects retriever}) = 0 \]

Final Answer