Discussion
If A and B are mutually exclusive and exhaustive events of \(\Omega\) such that P(A) = 2P(B), then P(A) = .........
Answer: C
P(A) = 2/3.
Mutually exclusive and exhaustive events cannot occur together and together make up the whole sample space, so their probabilities add to 1.
\[ \begin{aligned} P(A) + P(B) &= 1 \\ 2P(B) + P(B) &= 1 \Rightarrow P(B) = \tfrac{1}{3} \\ P(A) &= \tfrac{2}{3} \end{aligned} \]
1/3 is P(B), not P(A). 0 and 1 would make one of the events impossible, which contradicts P(A) = 2P(B) with both summing to 1.
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