A training program consists of three parts, each having a length of one month. F

Question

A training program consists of three parts, each having a length of one month. Fifty percent of the starting students immediately pass the first part after one month. 30% drop out before the end of the first month and 20% take the first part again. Seventy percent of the last group pass the first part after a second trial and the other 30% still drop out. Eighty percent of the students taking the second part pass this second part after the first trial. 10% drop out after the first trial and the other 10% move on after a second trial of the first part. Any student streaming into the third part of the training program will complete it successfully. Calculate the probability that a starting student will be successful.

Explanation / Answer

Suppose there 100 students in the batch. Out of them 50% directly pass in the first part. so 50 students pass immediately in the first part in the first trial. out of the remaining 50 students 30 students drop out and the remaning 20 students re-appear in the second trial to pass the 1st part. Of the 20 students 70% was able to pass the 2nd trail to get ove rthe 1st part, so 20*70%=14 students succeed in the 1st part and the remaining (20-14)=6 students again drop out. So total (14+50) = 64 students proceed fro the 2nd part. out of them 80% directly pass and 10% pass after the 2nd trial of the 2nd part. so total 64*(80%+10%)= 57.6 students proceed for the 3rd part. Out of them all pass in 3rd part.

So out of 100 students 57.6 student is able to clear all the 3 parts.

So probability that a starting student pass all the entire exam = 57.6/100 = 0.576

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