The true-false exam

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A student takes a true – false examination consisting of 10 questions. He is completely unprepared so he plans to guess each answer. The guesses are to be made at random. For example, he may toss a fair coin and use the outcome to determine his guess.
a. Compute the probability that he guesses correctly at least five times.
b. Compute the probability that he guesses correctly at least nine times.
c. What is the smallest n such that the probability of guessing at least n correct answers is
less than &?

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