Q. 2

# Two marbles are drawn successively from a box containing 3 black and 4 white marbles. Find the probability that both the marbles are black if the first marble is not replaced before the second draw.

Given: A box containing 3 black and 4 white marbles .Each trail is independent of the other trial.

Hence the sample space is given by S = {1B,2B,3B,1W,2W,3W,4W}

To find: the probability that both the marbles are drawn are black.

Let , success : marble drawn is black.i.e

Now , the Probability of success in the first trial is

P1(success) =

Probability of success in the second trial without replacement of the first draw is given by

P2(success) =

Hence , the probability that both the marbles are drawn are black ,with each trial being independent is given by

P1 P2 = =

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