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
3
7
Now , the Probability of success in the first trial is
P1(success) =
3
7
Probability of success in the second trial without replacement of the first draw is given by
P2(success) =
2
6
Hence , the probability that both the marbles are drawn are black ,with each trial being independent is given by