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Q.
$P(E\, \cap\, F)$ is equal to
Probability - Part 2
Solution:
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
$P\left(E\cap F\right) = P\left(F\right).P\left(E|F\right)\quad\ldots\left(i\right)$
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, $P\left(E\cap F\right) = P\left(E\right). P\left(F/F\right)\quad\ldots\left(ii\right)$