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Q&A If C = Calvin wins the match, and $X \thicksim Bin(2, p) =$ how many of the first 2 games he wins — then why P(C|X = 1) = P(C)?

posted 3y ago by Peter Taylor‭

Answer

#1: Initial revision by $user avatar$ Peter Taylor‭ · 2022-01-05T11:14:44Z (almost 3 years ago)

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The key is

> the first player to win two games more than his opponent wins the match

$P(C \mid X = 1)$ describes the situation when Calvin has won 1 of the first two matches: so the opponent won the other match, and they're currently even. Since a 1-1 score is equivalent to a 0-0 score for the purposes of winning, the probability that Calvin wins from a 1-1 situation is the same as the probability that Calvin wins from a 0-0 situation.

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