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!