The glimpse tells us that there is at least one heart, so if A is the event that we had two aces and H is the event that we had at least one heart, then what we need to know is whether P(A) and P(A|H) differ.

The latter quantity is a conditional probability, the probability that A occurs given that H occurs; it can be computed using the formula P(A|H) = P(A&H) / P(H), where A&H is the event that the opponent has both two aces and at least one heart.

After computing the probabilities P(A&H)=1/442 and P(H)=15/34, it follows that P(A)=1/221 and P(A|H)=1/195, which is more than 1/221.

So if there is at least one heart then the probability of getting two aces is higher.

Barb said she didn’t understand this “conditional probablity” stuff and demanded a simpler explanation because her “intuition” said that there should be no difference.

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