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Compute P(A>B) for m- and n-sided dice | Reddit Interview Question

Q: Compute P(A>B) for m- and n-sided dice

This question evaluates understanding of probability theory and discrete combinatorics, specifically reasoning about pairwise outcomes and deriving a parameterized closed-form expression for P(A > B) when A and B are m- and n-sided dice.

Sep 19, 2025, 12:00 AM

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Two fair dice are rolled independently:

Die A has m faces labeled $1,2,\dots,m$ .
Die B has n faces labeled $1,2,\dots,n$ .

Each face is equally likely.

Derive a closed-form expression for $\mathbb{P}(A > B)$ as a function of $m$ and $n$ .
Optionally, provide a simple Python function to compute it (either via the closed form or via counting).

Compute P(A>B) for m- and n-sided dice

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Compute P(A>B) for m- and n-sided dice

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