MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A bag contains 4 black and 6 white balls. A ball is drawn at random.
(i) Find the probability that the first ball drawn is white.
(ii) The ball drawn is not replaced. A second ball is then drawn. Calculate the probability that both the first and the second balls are white.
(iii) Now assume instead that the first ball is replaced before drawing the second ball. Calculate again the probability that both balls drawn are white.
(iv) Using the results of parts (ii) and (iii), examine whether the events “first ball is white” and “second ball is white” are independent in each of the two situations (with and without replacement). Give reasons for your answer.