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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