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.
