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 we have a batch of 100 students. Acoording the question

1st part :

50 % pass immediately. So 50 students is passed immediately. Out of the 50 students remaining , 30 students drop out and 20 students re-appeared in the 1st part for a second trial to get over it. Out of that 20, 70% passed in 2nd trial, so 20*70% = 14 students passed in the 2nd trial of the 1st part and they will proceed to the 2nd part. and the remaining (20-14) =6 students are dropping out. So after the 1st part (50+14) =64 students are progressing for the 1st part.

2nd part :

Out of the 64 students moving into 2nd part, 80% of them i.e 64*80%= 51.2 students pass directly in the 1st trial of the 2nd part and 10% of them = 64*10%=6.4 students pass after a 2nd trial of the 2nd part. So total number of students passed out of 54 in the 2nd part is (51.2+6.4)=57.6

3rd part:

All the students heading in 3rd part succeed in the 3rd part.

So total number students completing all the 3 parts out of 100 students = 57.6

So the the probability that a starting student will be successful = 57.6/100 = 0.576 (ANSWER)

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