Probabilities in an infinite game [Hinglish] | Probability | Grade 12 | Math | Khan Academy

In this video, we analyze the probabilities of winning a game that could potentially continue infinitely. We'll focus on a classic example where two players, A and B, take turns throwing a die, with the first to roll a '6' declared the winner. We will calculate their respective probabilities of winning using two different powerful methods: setting up a recursive probability equation, and summing an infinite geometric series.

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Timestamps:
00:00 Problem: A and B throw a die alternatively; first to get a '6' wins. A starts.
01:30 Method 1: Recursive Probability. Setting up an equation for A's win probability.
05:00 Method 2: Infinite Geometric Progression. Summing the probabilities of A winning on the 1st, 3rd, 5th... throw.
05:45 Finding the respective probabilities of A and B winning.

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Created by
Ashish Gupta