In a test there are ten multiple choice questions. For each question there is a choice of

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In a test there are ten multiple choice questions. For each question there is a choice of four answers, only one of which is correct. A student guesses each of the answers.

(a) Find the probability that he gets more than seven correct. He needs to obtain over half marks to pass and each question carries equal weight.

(b) Find the probability that he passes the test.

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