Q. 6

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.

Answer :

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 = =


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