**Question:**A pet store has 7 puppies, including 4 poodles, 2 terriers, and one retriever. If Rebecca and Aaron (in that order) each select one puppy at random, with replacement (they may both select the same one) find the probability of them both selecting a retriever?

Let

P = poodles = 4

T = terriers = 2

R = retriever = 1

Since each dog is equally likely to be picked,

P(P) = 4/7

P(T) = 2/7

P(R) = 1/7

So the probability that Rebecca will choose a retriever is 1/7. Likewise, the probability that Aaron will choose a retriever is also 1/7. The probability that both Rebecca AND Aaron choose a retriever represents their intersection.

Let

R = Rebecca

A = Aaron

P(R∩A) = P(R)P(A) (since the events are independent)

=(1/7)(1/7)

=1/49

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