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Question

A student is given a test with 8 items of true-false type. If he gets 6 or more items correct, he is declared pass. Given that he guesses the answer to each item, compute the probability that he will pass in the test.

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Solution

P(correct) =12 P(incorrect) =12

P(pass) = P(correct =6 ) + P(correct =7 ) + P(correct =8)

=8C6(12)6(12)2+8C7(12)7(12)+8C8(12)8(12)0

=(8C6+8C7+8C8)(12)8

=(28+8+1)28

=37256

=0.144

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