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

It is given that a box contains 3 black and 4 white marbles where each trial is independent of the other

Sample space S = {1B, 2B, 3B, 1W, 2W, 3W, 4W}

Consider success marble drawn is black = 3/7

So the probability of success in the first trial

P₁ (success) = 3/7

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

P₂ (success) = 2/6

So the probability that both the marbles drawn are black, with each trial being independent