The Longest Expected Match

★ 6/10combinatorics Extrema Counting probability

Problem

Two players compete in a series of games; in each game, player $1$ wins with probability $p_1$ (where $0 < p_1 < 1$ ) and player $2$ wins with probability $p_2 = 1 - p_1$ . The first player to win three games wins the match, and the games are independent. Let $X$ be the total number of games played. Find the maximum possible value of $E(X)$ .

Answer

Solution

Difficulty	6/10
Topics	combinatorics, Extrema, Counting, probability

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