A pet store has 1111 ​puppies, including 44 ​poodles, 44 ​terriers, and 33 retrievers. If Rebecka and​ Aaron, in that​ order, each select one puppy at random with replacement​ (they may both select the same​ one), find the probability that they both select a poodle.
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Part 1
The probability is enter your response here.
​(Type an integer or a simplified​ fraction.)

The problem asks to find the probability that both Rebecka and Aaron select a poodle, with replacement.

### Step 1: Probability of selecting a poodle

- The total number of puppies is 1111.
- The number of poodles is 44.

So, the probability that one person (Rebecka or Aaron) selects a poodle is:

\[
P(\text{poodle}) = \frac{44}{1111}
\]

### Step 2: Probability that both select a poodle

Since the selections are independent (because of replacement), the probability that both Rebecka and Aaron select a poodle is:

\[
P(\text{both poodles}) = P(\text{Rebecka selects poodle}) \times P(\text{Aaron selects poodle})
\]

\[
P(\text{both poodles}) = \frac{44}{1111} \times \frac{44}{1111}
\]

\[
P(\text{both poodles}) = \frac{44 \times 44}{1111 \times 1111}
\]

\[
P(\text{both poodles}) = \frac{1936}{1234321}
\]

Thus, the probability that they both select a poodle is:

\[
\boxed{\frac{1936}{1234321}}
\]

Let me know if you want more details or have any questions!

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Here are five related questions for further practice:

1. What is the probability that both select a terrier?
2. What is the probability that Rebecka selects a terrier and Aaron selects a poodle?
3. What is the probability that neither selects a poodle?
4. If the selection was without replacement, how would the probability change?
5. What is the probability that Rebecka selects a retriever and Aaron selects any puppy other than a retriever?

**Tip:** When dealing with "with replacement" problems, each event remains independent, so the total probability is just the product of individual probabilities!

A pet store has 1111 puppies, including 44 poodles, 44 terriers, and 33 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random with replacement (they may both select the same one), find the probability that they both select a poodle.

Find the probability that both Rebecka and Aaron select a poodle from a pet store with 1111 puppies, including 44 poodles. This problem covers the concept of independent events and the multiplication rule for probability. Suitable for students in Grades 9-12.

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