If A and B are any two events such that P(B) = P(A and B), then which of the following is correct
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $P(A|B) = 1$
$P(B)=P(A\cap B)$
$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$
$P(A\cap B)=P(B)$ gives
$P(A\mid B)=\frac{P(B)}{P(B)}$
$P(A\mid B)=1$
B is therefore a subset of A because B occurs only when A occurs.
Final answer: $P(A\mid B)=1$