Problem

A pet store has 8 puppies, including 3 poodles, 2 terriers, and 3 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement, find the probability that Aaron selects a retriever, given that Rebecka selects a poodle. The probability is (Type an integer or a fraction.)

Solution

Step 1 :The probability that Rebecka selects a poodle is \(\frac{3}{8}\), since there are 3 poodles out of 8 puppies.

Step 2 :If Rebecka selects a poodle, there are now 7 puppies left, including 3 retrievers. So the probability of Aaron selecting a retriever is \(\frac{3}{7}\).

Step 3 :The probability of both events happening is \(\frac{3}{8} \times \frac{3}{7} = \frac{9}{56}\).

Step 4 :The probability of Aaron selecting a retriever given that Rebecka selects a poodle is therefore \(\frac{9}{56} \div \frac{3}{8} = \frac{6}{7}\).

Step 5 :Final Answer: The probability that Aaron selects a retriever, given that Rebecka selects a poodle is \(\boxed{\frac{3}{7}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/36949/

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