Under the \"no pass, no play\" rule for athletes, an athlete who fails a course

Question

Under the "no pass, no play" rule for athletes, an athlete who fails a course is diqualified 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 again in the next time period is 0.5. If 20% of the athletes have been disqualified before, what is the unconditional probability that an athlete will be disqualified during the next grading period?

Explanation / Answer

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]

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