Question

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.

Answer 1

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\(\frac{3}{7}\)

Now , the Probability of success in the first trial is

P₁(success) = \(\frac{3}{7}\)

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

P₂(success) = \(\frac{2}{6}\)

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