HMMT 2012 U5

Guts
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Mr. Canada chooses a positive real $a$ uniformly at random from $(0,1]$ , chooses a positive real $b$ uniformly at random from $(0,1]$ , and then sets $c=a /(a+b)$ . What is the probability that $c$ lies between $1 / 4$ and $3 / 4$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{2}{3}

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