In a race, there are three contestants: A, B, and C. The winning probabilities are as follows;

Question

In a race, there are three contestants: A, B, and C.
The winning probabilities are as follows;
P(A)=2P(B), that is to say the winning probability of A is twice the winning probability of B.
Also, P(B)=3P(C).
If only one person wins (ties are not possible), calculate the probability of winning for each person

Answer 1

We know that

 

Pr(A)=2Pr(B),

 

 Pr(B)=3Pr(C);

 

hence, Pr(A)=6Pr(C).

 

But Pr(A)+Pr(B)+Pr(C)=1.

 

 6Pr(C)+3Pr(C)+Pr(C)=1.

 

 

10 Pr(C)=1

Pr(C)=1/10

So, Pr(C)=1/10

 

Pr(B)=3 Pr(C)=1(1/10)=3/10

 

Pr(A)=6 Pr(C) =6(1/10)=6/10