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11 March, 14:20

Suppose that you believe that contractor 1 is twice as likely to win as contractor 3 and that contractor 2 is three times as likely to win as contactor 3. What are the probabilities of winning for each contractor?

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  1. 11 March, 18:01
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    probability that contractor 1,2 and 3 win is 33%,50% and 17% respectively

    Step-by-step explanation:

    assuming that there are no other contractors then:

    probability that 1, 2 or 3 win = 1

    denoting as X = probability that contractor 3 wins, then assuming that only one wins, we have

    probability that 1, 2 or 3 win = 1

    probability that contractor 1 wins + probability that contractor 2 wins + probability that contractor 3 wins = 1

    2*P (X) + 3*P (X) + P (X) = 1

    6*P (X) = 1

    P (X) = 1/6

    then

    -probability that contractor 1 wins = 2/6 (33%)

    -probability that contractor 3 wins = 3/6 (50%)

    -probability that contractor 3 wins = 1/6 (17%)
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