A probability problem by A Former Brilliant Member

One bag contains 5 5 white balls and 4 4 black balls; another bag contains 4 4 white balls and 7 7 black balls. If one ball is drawn from each bag, find the probability that both are white. Give your answer correct to three decimal places.


The answer is 0.202.

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1 solution

The desired probability is

P = ( 5 5 + 4 ) ( 4 4 + 7 ) = ( 5 9 ) ( 4 11 ) = 20 99 P=\left(\dfrac{5}{5+4}\right)\left(\dfrac{4}{4+7}\right)=\left(\dfrac{5}{9}\right)\left(\dfrac{4}{11}\right)=\dfrac{20}{99}\approx 0.202 \color{#D61F06}\boxed{0.202}

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