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?

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%)