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Distributionshard
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Let XXX and YYY be independent Uniform(0,1)\text{Uniform}(0, 1)Uniform(0,1) random variables. Find the conditional probability P(X+Y≤1.5∣X+Y≥0.5)P(X+Y \le 1.5 \mid X+Y \ge 0.5)P(X+Y≤1.5∣X+Y≥0.5).