Any athlete who fails the Anonymous State University’s male soccer fitness test

Question

Any athlete who fails the Anonymous State University’s male soccer fitness test is automatically dropped from the team. Last year, Peter Parker 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 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 40% of the athletes who take the test are fit enough to play soccer. Assuming these estimates are correct, what is the probability that Peter was justifiably dropped?

Explanation / Answer

Here, we are given that:

P( fail | unfit ) =1 and P( fail | fit ) = 0.5

Also, we are given that: P( fit ) = 0.4

Therefore using the law of total probability, we get:

P( fail ) = P( fit )P( fail | fit ) + P( unfit )P( fail | unfit )

P( fail ) = 0.4*0.5 + 0.6*1 = 0.8

Therefore using bayes theorem now we get:

P( fit | fail ) = P( fit )P( fail | fit ) / P( fail ) = 0.2 / 0.8 = 0.25

P( unfit | fail ) = 1 - 0.25 = 0.75

Therefore the probability that Peter was justifiably dropped is computed as the probability that he failed the test given that he was unfit which is computed to be 0.75

Therefore 0.75 is the required value here.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.