A pet store has 4 poodles, 3 terriers, and 2 retrievers. If Rebecca and Aaron (in that order) each select a puppy at random, without replacement, what is the probability that Aaron selects a retriever given that Rebecca selects a poodle?

In this task you have 2 events and you are looking for a conditional probability. The first event is "Rebecca chooses a poodle". The probability of this event is

`P(R_p)=4/9`

because among 9 dogs there are 4 poodles.

The second event is "Aaron selects a retriever".
This event has a probability of `P(A_r)=2/8`, because after Rebecca's choice there are 8 pets in total and among them there are 2 retrievers.

To calculate probability of both events ("Rebeca selects a poodle and Aaron selects a retriever") you have to multiply both calculated probabilities:

`P=P(R_p)*P(A_r)=4/9*2/8=4/9*1/4=1/9`

There are 2 ways of interpreting this question...

I the understand the question as asking just about Aaron's choice. The fact that Rebecca has already chosen a poodle means that there are 8 puppies left.

So, just for Aaron, the probability is:

P(retriever) = `2/8 = 1/4`

However, if the question is to be read as;

"What is the probability that Rebecca chooses a poodle and Aaron chooses a retriever in this order", then we need to include Rebecca's choice.

P(poodle,retriever) = `4/9 xx2/8`

=`1/9`