EMP Q.32

0. A and B throw alternately with a pair of dice. A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6. If A begins then his chance of winning is

  • Option : B
  • Explanation : The sum 6 can be obtained as follows:
    (1,5), (2, 4), (3, 3), (4, 2), (5, 1), i.e. in 5 ways.
    Probability of A's throwing 6 with 2 dice = 5/36
    Probability of A's not throwing 6 = 31/36
    Similarly, probability of B's throwing 7 = 6/36, i.e. 1/6
    Probability of B's not throwing 7 = 5/6
    Now A can win, ifhe throws 6 in the first, third,
    fifth, seventh etc. throws.
    Chance of A's winning

    Probability

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