On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Solution

Here n = 5
$straight p space equals 1 third comma space space straight q space equals space 1 minus straight p space equals space 1 minus 1 third space equals space 2 over 3$
P(four or more correct answers) = P(4) + P(5)
$equals space straight C presuperscript 5 subscript 4 space open parentheses 2 over 3 close parentheses space open parentheses 1 third close parentheses to the power of 4 space plus space straight C presuperscript 5 subscript 5 space open parentheses 1 third close parentheses to the power of 5 space equals space 5 over 1 cross times 2 over 3 cross times 1 over 81 plus space 1 space cross times space 1 over 243 space equals space 10 over 243 plus 1 over 243 space equals 11 over 243$

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Probability

On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

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