Conditioned Die

Question

A fair die is rolled and you are told the result is even. What is the probability it is a 6?

Accepted Answer

The information "even" restricts the sample space to 2, 4, 6, all equally likely (conditioning on an event preserves the relative likelihoods of the outcomes inside it). So P(6 mid texteven) = fracP(6)P(texteven) = frac1/61/2 = frac13. Trivial, but the formal version, P(A mid B) = fracP(A cap B)P(B), is the single most-used identity in trading interviews. If you can't apply it reflexively, harder conditional questions will sink you.

Conditioned Die

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