Any athlete who fails the Enormous State University's women's soccer fitness test is automatically dropped from the team. Last year, Mona Header failed the test, but claimed that this was due to the early hour. (The fitness test is traditionally given at 5 AM on a Sunday morning.) In fact, a study by the ESU Physical Education Department suggested that 50% of athletes fit enough to play on the team would fail the soccer test, although no unfit athlete could possibly pass the test. It also estimated that 41% of the athletes who take the test are fit enough to play soccer. Assuming these estimates are correct, what is the probability that Mona was justifiably dropped Please, round your answer to four decimal places.
A)0.205
B) 0.2579
C) 0.7421
D) 0.09
E) 0.2217

Question

Any athlete who fails the Enormous State University's women's soccer fitness test is automatically dropped from the team. Last year, Mona Header failed the test, but claimed that this was due to the early hour. (The fitness test is traditionally given at 5 AM on a Sunday morning.) In fact, a study by the ESU Physical Education Department suggested that 50% of athletes fit enough to play on the team would fail the soccer test, although no unfit athlete could possibly pass the test. It also estimated that 41% of the athletes who take the test are fit enough to play soccer. Assuming these estimates are correct, what is the probability that Mona was justifiably dropped  Please, round your answer to four decimal places.  
A)0.205
B) 0.2579
C) 0.7421
D) 0.09
E) 0.2217

Quizplus · Accepted Answer

The probability that Mona was justifiably dropped is the probability that she is not fit enough to play soccer, given that she failed the test. This is equal to the probability that she is not fit enough to play soccer multiplied by the probability that she failed the test given that she is not fit enough to play soccer. The probability that she is not fit enough to play soccer is 1 - 0.41 = 0.59. The probability that she failed the test given that she is not fit enough to play soccer is 1.0. Therefore, the probability that she was justifiably dropped is 0.59 * 1.0 = 0.59.

Any Athlete Who Fails the Enormous State University's Women's Soccer