Question

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 1

It is given that an urn contains 5 white and 8 black balls with each trial being independent of the other.

Consider success in the first draw be getting 3 white balls

So the probability of success in the first trial

Consider the success in the second draw be getting 3 black balls

So the probability of success in the second trial without replacement of the first draw

Here the probability that the first draw gives 3 white and the second draw gives 3 black balls with each trial being independent