A student is given a true-false examination with 8 questions. If he gets 6 or more correct answers, he passes the examination. Given that the guesses at the answer to each question, compute the probability that he passes the examination.

Solution

Here n = 8, $straight p space equals space 1 half comma space space straight q space equals space 1 half$
P (passing the examination) =P(6) + P(7) + P(8)
$equals space straight C presuperscript 8 subscript 6 space open parentheses 1 half close parentheses squared space open parentheses 1 half close parentheses to the power of 6 space plus space straight C presuperscript 8 subscript 7 space open parentheses 1 half close parentheses space open parentheses 1 half close parentheses to the power of 7 space plus space straight C presuperscript 8 subscript 8 space open parentheses 1 half close parentheses to the power of 8 space equals space open parentheses 1 half close parentheses to the power of 8 space open square brackets straight C presuperscript 8 subscript 6 plus straight C presuperscript 8 subscript 7 plus straight C presuperscript 8 subscript 8 close square brackets space equals open parentheses 1 half close parentheses to the power of 8 space open square brackets fraction numerator 8 cross times 7 over denominator 1 cross times 2 end fraction plus 8 over 1 plus 1 close square brackets space equals 1 over 256 left parenthesis 28 plus 8 plus 1 right parenthesis space equals space 37 over 256$

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Probability

A student is given a true-false examination with 8 questions. If he gets 6 or more correct answers, he passes the examination. Given that the guesses at the answer to each question, compute the probability that he passes the examination.

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