An urn contains 5 white and 8 black balls. Two successive drawings of 3 balls at a time are made such that the balls drawn in the first draw are not replaced before the second draw. Find the probability that the first draw gives 3 white balls and the second draw gives 3 black balls.
Given: An urn containing 5 white and 8 black balls .Each trial is independent of the other trial.
To find: the probability that the first draws gives 3 white and the second draw gives 3 black balls.
Let , success in the first draw be getting 3 white balls.
Now , the Probability of success in the first trial is
P1(success) = 
=
=
Let success in the second draw be getting 3 black balls.
Probability of success in the second trial without replacement of the first draw is given by
P2(success) =
=
=
Hence , the probability that the first draws gives 3 white and the second draw gives 3 black balls,with each trial being independent is given by
P1
P2 = 
= 