Multiple choice

A and B roll a die successively till one of them gets a six. What are the chances of A` s winning if he starts the game?

  1. 4/11

  2. 6/11

  3. 8/11

  4. 9/11
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Probability of rolling a 6 is 1/6, not rolling is 5/6. A wins on 1st, 3rd, 5th... turn. P(A wins) = 1/6 + (5/6)(5/6)(1/6) + ... = (1/6) / (1 - 25/36) = (1/6) / (11/36) = 6/11.

AI explanation

The probability of rolling a six is 1/6, so the probability of not rolling a six is 5/6. Because A starts, his probability of winning is an infinite geometric series: 1/6 + (5/6)(5/6)(1/6) + (5/6)^4(1/6) + ... . Using the sum of an infinite geometric series formula, S = a / (1 - r), we get (1/6) / (1 - 25/36). This simplifies to (1/6) / (11/36), which equals 6/11.

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