ex215Under the no pass no play rule for athletes an athlete

ex2-15)Under the \"no pass, no play\" rule for athletes, an athlete who fails a course is disqualified from participating in sports activities during the next grading period. Suppose the probability that an athlete who has not previously been disqualified will be disqualified is 0.11 and the probability that an athlete who has been disqualified will be disqualified again in the next time period is 0.5. If 40% of the athletes have been disqualified before, what is the unconditional probability that an athlete will be disqualified during the next grading period? (Enter your answer to three decimal places.)

Solution

Let

B = has been disqualified before
D = will be disqualified

Hence,

P(D) = P(B) P(D|B) + P(B\') P(D|B\') = 0.20*0.5 + (1-0.20)*0.11 = 0.188 [ANSWER]