https://file.aiquickdraw.com/mathbot/file/1729055341742wdkg90ax.jpg

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.

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

Solve the probability problem of Aaron selecting a retriever, given that Rebecka selects a poodle, in a pet store with 12 puppies. Learn how to use conditional probability and calculate the probability as 4/11. Suitable for Grades 8-10.

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