If A and B are two events such that \(P(A) = 0.8\) and \(P(B|A) = 0.5\), then \(P(A \cap B)\) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.4
By the multiplication theorem of probability:
\( P(A \cap B) = P(A) \times P(B|A) \)
\( = 0.8 \times 0.5 \)
\( = 0.4 \)
Why the other options are incorrect
Option (2) 0.625 — Incorrect. This is \(\frac{0.5}{0.8}\), a division where a product is needed.
Option (3) 0.3 — Incorrect. This is \(0.8 - 0.5\), a difference where a product is needed.
Option (4) 0.2 — Incorrect. This is \(1 - 0.8\), the probability that A does not occur.