In a throw of 4 dice, find the probability that at least one die shows up 4.

Solution

Let p be the probability of throwing 4
$therefore space space space space straight p space equals space 1 over 6 comma space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 over 6 space equals space 5 over 6$
P(at least one die shows up) = 1 - P(0)
$equals space 1 minus straight C presuperscript 4 subscript 0 space open parentheses 1 over 6 close parentheses to the power of 0 space open parentheses 5 over 6 close parentheses to the power of 4 space equals space 1 minus space 1 space cross times space 1 space cross times space 625 over 1296 space equals space 1 minus 625 over 1296 space equals space fraction numerator 1296 minus 625 over denominator 1296 end fraction space equals 671 over 1296.$

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Probability

In a throw of 4 dice, find the probability that at least one die shows up 4.

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