Q. A candidate takes three tests in succession and the probability of passing the first test is . The probability of passing each succeeding test is or according as he passes or fails in the preceding one. The candidate is selected, if he passes atleast two tests. The probability that the candidate is selected, is

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Solution:

Required probability
Probability of passing two test
Probability of passing all three test
(passing I and II tests and fail in third test)
(passing Ist test, fail in II test and passing in Illrd test)
(fail in I test, passing in Ilnd and IIlrd tests)
(passing in all three tests)