Find the probability of getting 5 exactly twice in 7 throws of a die.

Solution

Here, n = 7
p = P(5) = $1 over 6 comma$ $straight q space equals space 1 minus 1 over 6 space equals 5 over 6$
P(exactly twice) = $straight P left parenthesis 2 right parenthesis space equals space straight C presuperscript 7 subscript 2 space space open parentheses 5 over 6 close parentheses to the power of 5 space open parentheses 1 over 6 close parentheses squared space equals space fraction numerator 7 cross times 6 over denominator 1 cross times 2 end fraction cross times 5 to the power of 5 over 6 to the power of 5 cross times 1 over 6 squared space equals space 21 space open parentheses 5 to the power of 5 over 6 to the power of 7 close parentheses.$

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Probability

Find the probability of getting 5 exactly twice in 7 throws of a die.

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