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In: Statistics and Probability

27. A single multiple-choice question has 5 choices, only one of which is correct. A student...

27. A single multiple-choice question has 5 choices, only one of which is correct. A student taking this test knows the answer with probability 0.8. If the student does not know the answer, he or she guesses randomly.
a) Find the probability that the student knew the answer, given that the question was answered correctly.
b) To pass the test a student must answer at least eight questions correctly from ten, what is the probability that the student will pass the test?

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