An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is :

Step-by-step solution

Total number of balls in the bag = 6 + 9 = 15 . Number of white balls = 6 . Number of black balls = 9 . Four balls are drawn at random at a time. The probability that first draw give four white balls C 4 6 C 4 15 = 1 91 The balls are not replaced. Now, the probability that second draw give four black balls C 4 9 C 4 11 = 21 55 The probability that the first draw give four white balls and second draw give four black balls = 1 91 × 21 55 = 3 715 Hence, the required probability is 3 715 .