a) If she knows the first answer, then you only have to worry about what's happening with three questions .....

So you want the probability of 3 correct guesses for 3 questions:

Pr(X = 3) where X follows a Binomial distribution with n = 3 and p = 1/2 ....... 1/8

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b) If she knows all the answers except one, then you only have to worry about what's happening with that one question .....

So you want the probability of 1 correct guess for 1 question ..... 1/2.