A pet store has 8 puppies, including 3 poodles, 2 terriers, and 3 retrievers. If Rebecka selects one puppy at random, the pet store replaces the puppy with a puppy of the same breed, then Aaron chooses a puppy at random. Find the probability that they both select a poodle.

Question

Aden Peck

Mathematics

8 August, 04:36

A pet store has 8 puppies, including 3 poodles, 2 terriers, and 3 retrievers. If Rebecka selects one puppy at random, the pet store replaces the puppy with a puppy of the same breed, then Aaron chooses a puppy at random. Find the probability that they both select a poodle.

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Answers (1)

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Rachel · Answer 1

9 / 64

Step-by-step explanation:

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

P (Rebecca chooses a poodle) = 3 / 8

- because among 8 dogs there are 3 poodles.

- The second event is "Aaron selects a poodle".

This event has a probability of that is equivalent to previous selection:

P (Aaron chooses a poodle) = 3 / 8

- Because after Rebecca's choice the chosen poodle is replaced with the poodle; hence, there are 8 pets in total and among them there are 3 poodles.

- To calculate probability of both events ("Rebeca selects a poodle and Aaron selects a poodle") with replacement you have to multiply both calculated probabilities - condition of independent events:

P (Aaron and Rebecca both select poodle) = 3 / 8 * 3 / 8

= 9 / 64