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A canditate takes three tests in succession and the probability of passing the first test is p . the probability of passing each succeeding test is p or

p/2 according as he passes or fails in the preceeding one. the candidate is selected if he passes atleast 2 tests. the probability that the candidate is selected is ?

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Notice that if is the probability of pass, then the probability of fail is .

The candidate can pass atleast 2 tests in 4 ways and the probabilities are given by : 1) passing all 3 tests : 2) passing first two tests and failing third test : 3) passing first test, failing second and passing third : 4) failing first test, passing second and third :

Add them up to get the probability for candidate to be selected :

We need to know the probability that he/she passes at least two tests. Let the three tests be named as A, B and C (in order). The required probability is where we have used . I am not so sure about it, in any case feel free to report it.