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.

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`