Question

$P(E\cap F)$ is equal to

• A. $P(E).P(F|E)$
• B. $P(F).P(E|F)$
• C. Both $(a)$ and $(b)$
• D. None of these

Answer 1

Answer: (C)

We know that, conditional probability of event $E$ given that $F$ has occurred is denoted by $P(E|F)$ and is given by
$P\left(E|F\right)=\frac{P\left(E\cap F\right)}{P\left(F\right)}$, $P\left(F\right)\ne 0$
From this result, we can write
$P\left(E\cap F\right)=P\left(F\right).P\left(E|F\right)\dots \left(i\right)$
Also, we know that
$P\left(F|E\right)=\frac{P\left(F\cap E\right)}{P\left(E\right)}$, $P\left(E\right)\ne 0$
Thus, $P\left(E\cap F\right)=P\left(E\right).P\left(F/F\right)\dots \left(ii\right)$