The problem in the image asks us to find the probability that Aaron selects a retriever, given that Rebecka selects a poodle. Let's break this down step by step.

Key Information:

• There are 10 puppies in total.
  • 2 poodles
  • 5 terriers
  • 3 retrievers
• Rebecka and Aaron select one puppy at random without replacement, meaning after Rebecka selects a puppy, there are 9 puppies left for Aaron to choose from.

Steps:

1. Rebecka's Selection:

   • The probability that Rebecka selects a poodle is $\frac{2}{10} = \frac{1}{5}$.

2. Aaron's Selection (Conditional Probability):

   • Given that Rebecka has already selected a poodle, there are 9 puppies remaining, consisting of:

     • 1 poodle (since one poodle has already been selected by Rebecka),
     • 5 terriers,
     • 3 retrievers.

   • Now, Aaron's selection is limited to these 9 puppies, and we are interested in the probability that Aaron selects a retriever. There are 3 retrievers out of the remaining 9 puppies, so the probability that Aaron selects a retriever is $\frac{3}{9} = \frac{1}{3}$.

Final Answer:

Since the problem asks for the probability that Aaron selects a retriever given that Rebecka has already selected a poodle, the answer is $\frac{1}{3}$.

Would you like a more detailed breakdown, or do you have any other questions? Here are some related questions to consider:

1. What would the probability be if Rebecka selected a terrier instead?
2. How does the probability change if they select puppies with replacement?
3. What is the probability that both Rebecka and Aaron select retrievers?
4. How would you calculate the probability if there were 4 retrievers instead of 3?
5. What if Aaron is given the first choice? How would the problem change?

Tip: When dealing with conditional probabilities, always account for how the total number of choices changes as selections are made!