For example, in the
experiment of drawing two cards one after the other, we may be interested in finding
the probability of the event ‘a king and a queen’ The probability of event EF is obtained
by using the conditional probability as obtained below :
We know that the conditional probability of event E given that F has occurred is
denoted by P(E|F) and is given by
P(E|F) = P(E
P(F)F) ,P(F) 0
∩
≠
From this result, we can write
P(E ∩ F) = P(F) P(E|F) (1)
Also, we know that
P(F|E) = P(F
P(E)E) ,P(E) 0
∩
≠
or
P(F|E) = P(E
P(E)F)
∩
 (since E ∩ F = F ∩ E)
Thus,
P(E ∩ F) = P(E)