Therefore, the probability that the
second ball drawn is black, given that the ball in the first draw is black, is nothing but
the conditional probability of F given that E has occurred i e P(F|E) = 9
14
By multiplication rule of probability, we have
P (E ∩ F) = P(E) P(F|E)
= 10
9
3
15
14
7
 
Multiplication rule of probability for more than two events If E, F and G are
three events of sample space, we have
P(E ∩ F ∩ G) = P(E) P(F|E) P(G|(E ∩ F)) = P(E) P(F|E) P(G|EF)
Similarly, the multiplication rule of probability can be extended for four or
more events