First head strictly sooner

MediumProbability Random Variables~5m

Bill and Bob each flip their own coin (heads probability $\tfrac13$ ) once per round, simultaneously, until each gets a first head. What is the probability that Bill gets his first head in strictly fewer flips than Bob?

Show hints (2)+

By symmetry $\mathbb{P}(\text{Bill sooner})=\tfrac12(1-\mathbb{P}(\text{tie}))$ .
A tie is both first-heads on the same round: $\sum_k[(2/3)^{k-1}(1/3)]^2 = 1/5$ .

Answer

Reveal answer →

0.4

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

Create a free account

Interview format: Market Maker, Numerical Reasoning Tests

First head strictly sooner

Answer

Related questions