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Question and answer bank question 1.10

A

alyaaredha

Member
in question 1.10 part i)b) we are asked to find he probability he passes the 5th exam, given that he fails the first three. The question seems pretty straightforward and I would assume that you calculate the probability using these 2 paths :
F-F-F-F-P or F-F-F-P-P getting (1-beta^2)(beta*alpha+(1-beta)*beta). The answer given is just (beta*alpha+(1-beta)*beta) and i can't seem to see why. Could anyone let me know where I went wrong?
Thank you!!
Aliaa
 
The paths you determined are correct:
The probability of first path is as below:
it is given that he fails first three so the Prob. of failing the fourth given he failed in third is (1-beta). Further, Prob. of passing the fifth given failed in fourth is beta. So the total probability of first path is beta*(1-beta).
Similarly, Prob. of second path is alpha*beta.
 
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