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The same number of tails

MediumProbabilityCombinatorics~5m

Two people each flip a fair coin 44 times. What is the probability that they get the same number of tails?

Show hints (2)+
  1. P(equal)=2−8∑k(4k)2\mathbb{P}(\text{equal})=2^{-8}\sum_k \binom{4}{k}^2.
  2. Vandermonde: ∑k(4k)2=(84)=70\sum_k\binom{4}{k}^2=\binom{8}{4}=70.

Answer

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0.2734 (± 0.001)

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Asked at: Jane Street, Two Sigma

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