A recent college graduate is planning to take a sequence of

A recent college graduate is planning to take a sequence of licensing exams for actuaries. If she passes the first exam, she may proceed to the second one and if she passes that one, she may proceed to the third one. If she fails any exam, she may not continue. The probability that she will pass the first exam is 0.9 and the conditional probability that she will pass the second exam given a pass on the first one is 0.8. The conditional probability that she will pass the third exam given success on the first two is 0.7.

What is the probability that she passes all three exams?

plz answer and explain why is this independent

Solution

The probability that she will pass the first exam is 0.9

the conditional probability that she will pass the second exam given a pass on the first one is 0.8.

The conditional probability that she will pass the third exam given success on the first two is 0.7.

probability that she passes all three exams

=> P(passes all three exams) = P(pass 1st) *P(2nd given 1st) *P(3rd given 2nd)

= 0.9*0.8*0.7

= 0.504 .................ANSWER

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Explantion:- These three events are dependent but these three probailities are independent.

P(2nd event given first one already pass) is Now become independent to 1st pass

I hope you got it.

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