medium   Probability

Parity Streaks

A release-checked medium problem for training Coins, Expected Value/LOTUS, Random Walk.

Question

Fix positive integers $h$ and $t$. What is the expected number of flips of a fair coin needed in order to either have $h$ more heads flipped than tails or $t$ more tails flipped than heads? Submit the result when $t = 10$ and $h=8$.

Practice focus

This Probability problem is tagged Coins, Expected Value/LOTUS, Random Walk. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.

Explore related collections

Reviewed questions in this area

easyBaby BoyReviewed

Probability · SIG, DE Shaw

easyBad BagelReviewed

Probability · SIG, Jane Street