Question

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that: (i) both the balls are white (ii) one ball is black and the other red (iii) both the balls are of the same colour. Select the correct answer from above options

Answer 1

There are total `7` white, `5` black and `4` red balls. So, there are total `16` balls. So, total number of ways drawing `2` balls are `C(16,2).` (i) Total number of ways both the ball drawn are white `= C(7,2)` `:.` Probability of drawing both white balls `= (C(7,2))/(C(16,2)) = 21/120 = 7/40`. (ii) Total number of ways one of the drawn ball is black and other is red `= C(5,1)*C(4,1)` `:.` Probability of drawing one black ball and one red ball `= (C(5,1)*C(4,1))/(C(16,2)) = 20/120 = 1/6.` (iii)Total number of ways both balls are of same colour `= C(7,2)+C(5,2)+C(4,2)` `:.` Probability of drawing both balls of same colour `= (C(7,2)+C(5,2)+C(4,2))/(C(16,2)) = (21+10+6)/(C(16,2)) = 37/120`