If E and F are two events such that P(E) = 0.7, P(F) = 0.4 and \(P(E\cap F) = 0.2\), then P(E|F) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{1}{2}\)
By the definition of conditional probability, the given event F goes in the denominator:
\( \displaystyle P(E|F) = \frac{P(E\cap F)}{P(F)} \)
\( \displaystyle = \frac{0.2}{0.4} = \frac{1}{2} \)
Why the other options are incorrect
Option (1) \(\displaystyle\frac{2}{7}\) — Incorrect. This is \(\frac{0.2}{0.7} = P(F|E)\), which divides by P(E) instead of P(F).
Option (3) \(\displaystyle\frac{1}{5}\) — Incorrect. This is \(P(E\cap F) = 0.2\) itself, not divided by P(F).
Option (4) \(\displaystyle\frac{7}{25}\) — Incorrect. This is \(P(E)P(F) = 0.28\), which is not a conditional probability at all.