An experiment yields 3 mutually exclusive and exhaustive events $A$, $B$ and $C$. If $P(A) = 2P(B)$ and $2P(C) = 3P(B)$, then $P(A)$ is equal to
Step-by-Step Solution
Key Concept: Use the property that mutually exclusive and exhaustive events sum to probability 1
Since events $A$, $B$, and $C$ are mutually exclusive and exhaustive, $P(A \cup B \cup C) = 1$. This means $P(A) + P(B) + P(C) = 1$. Given $P(A) = \frac{1}{2}P(A) + \frac{1}{4}P(A) + 1$, we solve: $\frac{11}{4}P(A) = 1$, so $P(A) = \frac{4}{11}$.
Correct Answer: D