Question

There are 15 dogs and 10 cats at an animal shelter. If a family decides to randomly select 5 animals to adopt, find the probability that the family selects 3 dogs and 2 cats.

A) 0.197
B) 0.317
C) 0.427
D) 0.537

Answer 1

The probability of selecting 3 dogs and 2 cats from an animal shelter with 15 dogs and 10 cats, calculated using combinations, is approximately 0.317.

Step-by-step explanation:

The subject of the question at hand is probability, which is a branch of mathematics that deals with the likelihood of different outcomes. To determine the probability that a family selects 3 dogs and 2 cats out of 15 dogs and 10 cats, we use the concept of combinations, as the order of selection does not matter.

The number of ways to choose 3 dogs from 15 is denoted by C(15,3), and the number of ways to choose 2 cats from 10 is denoted by C(10,2). The total number of ways to choose 5 animals from the 25 total animals is C(25,5).

Using these combinations, the probability of selecting 3 dogs and 2 cats is calculated as follows:

Probability = (C(15,3) * C(10,2)) / C(25,5)

After calculating the combinations, we compute:

Probability = (455 * 45) / 53130

Probability = 0.3169, which rounded to three decimal places equals 0.317, corresponding to option B.