For two events A, B
\(P(A \cup B) = \displaystyle\frac{7}{12}\), \(P(A) = \displaystyle\frac{5}{12}\), \(P(B) = \displaystyle\frac{3}{12}\). Then \(P(A \cap B) =\)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{1}{12}\)
By the addition theorem of probability,
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
So
\(P(A \cap B) = P(A) + P(B) - P(A \cup B)\)
\( \displaystyle = \frac{5}{12} + \frac{3}{12} - \frac{7}{12} \)
\( \displaystyle = \frac{1}{12} \)