Probability AIME Basic
2014


Problem - 84
An urn contains $4$ green balls and $6$ blue balls. A second urn contains $16$ green balls and $N$ blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is $0.58$. Find $N$.

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Solving $$\frac{4}{4+6}\times\frac{16}{16+N}+\frac{6}{4+6}\times\frac{N}{16+N}=\frac{58}{100}$$

gives answer $N=\boxed{144}$.

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