‹ Back to the paper
Solve the following.
Evaluate: P(A ∪ B) if 2P(A) = P(B) = 5/(13) and P(A|B) = 2/5
Evaluate: $P(A \cup B)$ if $2P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$
Answer
Answer
$P(A) = \frac{5}{26}$, $P(B) = \frac{5}{13}$.
$P(A\cap B) = P(A|B)\,P(B) = \frac{2}{5}\times\frac{5}{13} = \frac{2}{13}$
$P(A\cup B) = P(A) + P(B) - P(A\cap B) = \frac{5}{26} + \frac{10}{26} - \frac{4}{26} = \frac{11}{26}$
Hence $P(A\cup B) = \frac{11}{26}$.
Final answer: $\frac{11}{26}$