Question

The high school students who attend Springfield Women's Academy are eligible to try out for various teams within the athletic department. Students are 74% likely to try out for softball; 27% likely to try out for volleyball; 42% likely to try out for tennis; and 88% likely to try out for swimming. Many students choose to try out for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. What is the probability of the union of trying out for either volleyball or swimming?

A) 0.61
B) 0.91
C) 1.15
D) 0.24

Answer 1

To find the probability of the union of trying out for either volleyball or swimming, we need to add the probabilities of trying out for each sport and then subtract the probability of trying out for both sports to avoid double counting. The probability of the union of trying out for either volleyball or swimming is 0.91.

Step-by-step explanation:

To find the probability of the union of trying out for either volleyball or swimming, we need to add the probabilities of trying out for each sport and then subtract the probability of trying out for both sports to avoid double counting.

Given that the probability of trying out for volleyball is 27% and the probability of trying out for swimming is 88%, we can calculate:

Probability of trying out for either volleyball or swimming = Probability of trying out for volleyball + Probability of trying out for swimming - Probability of trying out for both = 27% + 88% - (27% * 88%)

Using the above formula, the probability of the union of trying out for either volleyball or swimming is 0.91, which corresponds to option B.