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Probability Problem

Posted By: Timothy Chow
Date: Thursday, 27 August 2009, at 6:03 p.m.

In Response To: Probability Problem (poseidon)

The reason that there can be controversy over this problem is that as posed, it is not quite a precise mathematical question. To make it a precise mathematical question, one has to introduce some extra assumptions. Many people aren't aware what tacit assumptions they're making, so they can get different answers from someone else who makes a different tacit assumption.

For example, one person might assume that in the first case, the friend is following the rule: "Look at both of my cards; if at least one of the two cards is an ace, then say `My hand contains an ace.' Otherwise, say nothing." Someone else might assume that the friend is following the rule, "Look at the first card I was dealt and ignore the second one. Note the value X of the card and announce, `My hand contains an X.'" Various other rules of varying plausibility can be invented, which can give varying answers for the probability. An extreme example would be the rule, "Look at both of my cards; if both are aces, then announce `My hand contains an ace.' Otherwise, say nothing." The problem as phrased does not preclude different rules of behavior, so there is room for argument about which rule of behavior was intended.

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