Question

There are 3 candidates in an election. Probability of winning election is 2 times a probability of B's are 3 times as probability of C. What is the probability if C's winning election?

• A. $\frac{2}{11}$
• B. $\frac{6}{11}$
• C. $\frac{1}{6}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{2}{11}$

Let $P\left(A\right)=x,P\left(B\right)=\frac{x}{2}P\left(C\right)=\frac{x}{3}$
$P\left(A\right)+P\left(B\right)+P\left(C\right)=1$
$\to x+\frac{x}{2}+\frac{x}{3}=1$
$\to 6x+3x+2x=6$
$\to x=\frac{6}{11}$
$P\left(C\right)=\frac{6}{3\times 11}=\frac{2}{11}$