Five coins against four: who gets more heads

Question

You flip five fair coins and I flip four fair coins. What is the probability that your number of heads is strictly greater than mine?

Short answer

$1/2$ . Since you have one more coin than me, you must end with either more heads than me or more tails than me, but not both. Swapping the labels heads and tails turns one event into the other, so each has probability $\tfrac12$ .

Adapted from Crack, Heard on the Street, Q4.3, p.37; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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