A pet store has 11 puppies, including 5 poodles, 2 terriers, and 4 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.

The probability that both Rebecka and Aaron select a poodle is 25/11 (0.20661).

Step-by-step explanation:

Step 1; We must calculate the probability that Rebecka will choose a poodle first. The total number of outcomes (total number of puppies) is 11. There are 5 poodles, 2 terriers, and 4 retrievers. So the number of favorable outcomes is the number of poodles there which equals 5.

So the probability that Rebecka will choose a poodle = 5/11.

Step 2; Now we calculate the probability of Aaron choosing a poodle. It will remain the same as Rebecka as any puppies selected will be replaced by a puppy of the same breed. So total number of outcomes (total number of puppies) is 11 while the number of favorable outcomes (number of poodles) is 5.

So the probability that Aaron will choose a poodle = 5/11.

Step 3; The probability that both Rebecka and Aaron will choose a poodle is the product of the probability of Rebecka getting a poodle and the probability of Aaron getting a puppy.

The probability that both will choose a poodle = 5/11 * 5/11 = 25/121 (0.20661).