A bag contains 5 white, 7 red and 18 black balls. If four balls are drawn one by one with replacement, what is the probability that at least one is white?

Solution

Here n = 4
Let p be the probability of drawing a white ball
$therefore space space straight p space equals space 5 over 20 space equals space 1 fourth comma space space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 fourth space equals 3 over 4$
P(at least one ball is white) = 1 - P(0)
$equals space 1 minus straight C presuperscript 4 subscript 0 space open parentheses 3 over 4 close parentheses to the power of 4 space equals space 1 minus 1 space cross times space 81 over 256 space equals fraction numerator 256 minus 81 over denominator 256 end fraction space equals space 175 over 256.$

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Probability

A bag contains 5 white, 7 red and 18 black balls. If four balls are drawn one by one with replacement, what is the probability that at least one is white?

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