Qm
Probability

Chance the first coin is heads given seven of ten

conditional-expectationsymmetrygiven-a-sumcoins

You flip ten fair coins and are told that exactly 77 of them came up heads.

Given that there are 77 heads in total, what is the probability that the first coin is heads?

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The theory behind this question.

Burnside's Lemma and Polya CountingSymmetry Shortcuts for Draws Without ReplacementThe Law of Total VarianceRegular Conditional DistributionsThe ABRACADABRA Problem

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