Question

Five dice are thrown simultaneously. If the occurrence of an even number is considered as a success, find the probability of at the most 3 successes.

Solution

Here n = 5, p = P(1, 3, 5) = $1 half comma space$ q = 1 - p = 1 - $1 half equals space 1 half$
P(atmost three successes) = 1 - [P(4) + P(5)]
$equals space 1 minus space open square brackets straight C presuperscript 5 subscript 4 space open parentheses 1 half close parentheses to the power of 4 space open parentheses 1 half close parentheses plus space space straight C presuperscript 5 subscript 5 space open parentheses 1 half close parentheses to the power of 5 close square brackets space equals space 1 minus 1 over 32 space open square brackets straight C presuperscript 5 subscript 4 space space plus space straight C presuperscript 5 subscript 5 close square brackets equals space 1 minus 1 over 32 left parenthesis 5 plus 1 right parenthesis space equals space 1 minus 3 over 16 space equals space 13 over 16$

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Probability

Five dice are thrown simultaneously. If the occurrence of an even number is considered as a success, find the probability of at the most 3 successes.

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