Matching a max and a min at zero

EasyProbability~4m

Two integers $x$ and $y$ are chosen independently and uniformly from $S = \{-10, -9, \dots, 9, 10\}$ . What is the probability that $\max\{0, x\} = \min\{0, y\}$ ?

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One side is always $\ge 0$ , the other always $\le 0$ . When can they be equal?
Only when both are $0$ : need $x\le0$ and $y\ge0$ . Count values (don't forget $0$ ).

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0.2744 (± 0.001)

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Asked at: Jane Street, SIG

Matching a max and a min at zero

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