Let's analyze the problem shown in the image:

Problem: A pet store has 12 puppies, including 3 poodles, 5 terriers, and 4 retrievers. Rebecka and Aaron, in that order, each select one puppy at random without replacement. We are asked to find the probability that Aaron selects a retriever, given that Rebecka selects a poodle.

Step-by-Step Solution:

1. Total puppies:
   There are 12 puppies in total.

2. Rebecka selects a poodle:
   There are 3 poodles, so the probability that Rebecka selects a poodle is: $P(\text{Rebecka picks a poodle}) = \frac{3}{12} = \frac{1}{4}$

3. Aaron selects a retriever after Rebecka picks a poodle: After Rebecka picks a poodle, there are 11 puppies left, with 4 retrievers remaining.

   The probability that Aaron selects a retriever from the remaining puppies is: $P(\text{Aaron picks a retriever}) = \frac{4}{11}$

4. Conditional Probability: The problem asks for the conditional probability that Aaron selects a retriever given that Rebecka has already selected a poodle. Since these events are independent once Rebecka picks a poodle, the conditional probability simplifies to: $P(\text{Aaron picks a retriever | Rebecka picks a poodle}) = \frac{4}{11}$

Thus, the probability that Aaron selects a retriever, given that Rebecka selects a poodle, is 4/11.

Would you like more details on any part of the explanation?

Here are some follow-up questions to deepen understanding:

1. What would the probability be if Rebecka selected a terrier instead of a poodle?
2. How would the probability change if there were 5 poodles instead of 3?
3. What is the probability that both Rebecka and Aaron select a retriever?
4. What is the probability that neither Rebecka nor Aaron selects a poodle?
5. If Aaron had to select from only terriers after Rebecka's selection, what would the probability be?

Tip: In probability problems, understanding "without replacement" is key. It means that after one selection, the total number of options changes, affecting subsequent probabilities.