Tuesday, April 29, 2014

Conditional probabilities and infinite fair lotteries

Suppose infinitely many independent fair coins are tossed. Let H be the event that exactly one of the coins is heads. Then conditionally on H, it looks like we have an infinite fair lottery: every coin is equally likely to be the heads one! So if one thinks (as one should) that infinite fair lotteries are incoherent, one also cannot conditionalize on null probability events like H.

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