Whose draw is larger?

MediumProbability~6m

Jimmy picks a number uniformly at random from $\{1, 2, \dots, 1000\}$ and, independently, Simon picks uniformly from $\{1, 2, \dots, 3000\}$ . What is the probability that Simon's number is strictly larger than Jimmy's?

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Condition on Jimmy's value $j$ : $\mathbb{P}[\text{Simon}>j]=(3000-j)/3000$ .
Average over $j\in\{1,\dots,1000\}$ using $\sum_{j=1}^{1000} j=\tfrac{1000\cdot1001}{2}$ .

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0.8332 (± 0.002)

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Interview format: Hedge Fund Quant, Prop Trading

Whose draw is larger?

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