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GATE 2015 EE – Question 39

Engineering Mathematics · Probability and Statistics: Conditional probability · 2 marks · Multiple choice

Two players, A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is

  1. 5/11
  2. 1/2
  3. 7/13
  4. 6/11

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Correct answer: (D) 6/11

Explanation

Player A wins on the first roll with probability $\frac{1}{6}$. Otherwise both miss, with probability $\left(\frac{5}{6}\right)^2$, and the game restarts. So $P = \frac{1}{6} + \frac{25}{36}P$, which gives $P = \frac{1/6}{11/36} = \frac{6}{11}$.