A bag contains X red balls and 5 green balls. Two balls are picked at random, one after the other, without replacement. If the probability of both balls being red is \(\frac{3}{7}\), what is the value of X?

Correct answer: 10

Solution

Without replacement, the probability of drawing two red balls is \(\frac{X}{X+5}\cdot\frac{X-1}{X+4}=\frac{3}{7}\). Solving this equation gives \(X=10\).

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