Multiple choice

A and B take turns in throwing two dice, the first who throws 10 gets the prize. Find their chances of winning, if A gets the first turn.

  1. 9/23

  2. 12/23

  3. 15/23

  4. 18/23
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum of two dice = 10: (4,6), (5,5), (6,4) -> 3 outcomes. P(win) = 3/36 = 1/12. P(lose) = 11/12. A wins on 1st, 3rd, 5th... turn. P(A) = 1/12 + (11/12)^2 * 1/12 + ... = (1/12) / (1 - (11/12)^2) = (1/12) / (1 - 121/144) = (1/12) / (23/144) = 12/23.

AI explanation

The probability of throwing a 10 with two dice is 3/36 = 1/12. Because A starts the game, the chance of A winning is an infinite geometric series: 1/12 + (11/12)^2(1/12) + (11/12)^4(1/12) + ... . Using the sum of an infinite geometric series formula, S = a / (1 - r), we get (1/12) / (1 - 121/144). This simplifies to (1/12) / (23/144), which equals 12/23.

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