Probability I · Conditional probability and independence
Independent rounds of a game have three possible results: win with probability 2/7…
Problem
Independent rounds of a game have three possible results: win with probability \(2/7\), loss with probability \(1/7\), and retry with probability \(4/7\). Play stops at the first win or loss. Find the probability of eventually winning, and justify that play terminates with probability one. Given that play stops on round n, find the probability that the terminal result is a win.
Hint
Split the eventual-win event by the first round's three outcomes.
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