A candidate has to pass three successive stages—written test
MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
A candidate has to pass three successive stages—written test (W), group discussion (G) and interview (I)—to be finally selected. The probability of passing the written test is 0.75. If the candidate passes the written test, the probability of passing the group discussion is 0.6. If the candidate passes both the written test and the group discussion, the probability of passing the interview is 0.8.
(i) Determine the probability that the candidate passes all three stages and is finally selected.
(ii) If 500 candidates appear for the written test, estimate the expected number of candidates who will be finally selected.
(iii) Find the probability that a candidate fails to clear at least one of the three stages.