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 45% 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? (Give your answer as a decimal rounded to two places.)

Answer 1

sel Let Event A= ployer is lit enough to play Event B player is not fit enough to play Event C = playey pass the soccer test Evento = playey fail in the soccer test It is given that, P(DA) = 0.50, P(0/B) = 1 PLA) =0.45 P(B) = 1-0.45 =0.55 p/mana was justifiably dropped) =P [Mana failed the last] » P/B/0) = P/O/B) :P (B) = P(018). P(8) [By Bayes Theorem [p(018). PLB)} 4[PLOADXP 167] > PlBlo) = 0.5SX) O-ssxi) +(0.45X0:50) 0:55 0775 2011 Soy Probability that monis Justifiably dropped is 0:11.