MathDB
2023 Fall LMT Speed p12 - flipping a weighted coin

Source:

March 2, 2024
combinatorics

Problem Statement

Sam and Jonathan play a game where they take turns flipping a weighted coin, and the game ends when one of them wins. The coin has a 89\frac89 chance of landing heads and a 19\frac19 chance of landing tails. Sam wins when he flips heads, and Jonathan wins when he flips tails. Find the probability that Samwins, given that he takes the first turn.
Proposed by Samuel Tsui