neetquant
Get started

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

Reveal answer →

0.2734 (± 0.001)

Create a free account to see the full worked solution and track your progress.

Create a free account

Interview format: Market Maker, Systematic & Data-Driven Trading

Related questions