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Question

In a race, 3 horses A,B,C are participating. The probability of A winning is twice the probability of B. The probability of winning B is twice the probability of C winning. Then find the probabilities of winning A,B and C.

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Solution

P(A) is the probability of A winning the race, P(B) is the probability of B winning the race and P(C) is the probability of C winning the race.
According to the given conditions, P(A)=2P(B) and P(B)=2P(C)
Also, P(A)+P(B)+P(C)=1 since either A,B or C has to win the race.
4P(C)+2P(C)+P(C)=1
P(C)=17
P(B)=27,P(A)=47

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