Interview Question: 3-Way Race

Sample Question #244 (probability theory)

Three horses are in a race. Horse A is twice as likely to win as horse B, which in turn is twice as likely to win as horse C. What is the probability that horse A will not win the race?

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One Response to Interview Question: 3-Way Race

  1. Brett says:

    ANSWER
     
    Let’s assume that nothing interrupts the race.
     
    Let Pr(horse C wins the race)=p. Then Pr(horse B wins)=2p and Pr(horse A wins)=4p. Since Pr(any horse wins)=1, we see immediately p=1/7 and Pr(horse A does not win)=1-4p=3/7.
     

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