Previous Year Questions

Let total number of balls in the bag = 24x

Probability of drawing a blue colour ball = (5/24)

Total blue colour balls = 5x

Total red and green colour balls = 24x - 5x = 19x

Total red colour balls = 19x * (9/19) = 9x

Total green colour balls = 19x * (10/19) = 10x

From I:

Average of total number of balls of all the three colours-

(5x + 9x + 10x)/3 = 8

24x = 24

x = 1

Total balls in the bag = 24x = 24

Statement I alone is sufficient.

From II:

Probability that two drawn balls are of green colour = ^10xC₂/^24xC₂ = 15/92

5x(10x - 1)/12x(24x - 1) = 15/92

23x(10x - 1) = 9x(24x - 1)

230x - 23 = 216x - 9

14x = 14

x = 1

Total balls in the bag = 24x = 24

Statement II alone is sufficient.

From III:

Probability that one ball is drawn and that ball is either red or blue-

(^9xC₁ + ^5xC₁)/^24xC₁ = 7/12

(9 + 5)/24 = 7/12

14/24 = 7/12

1 = 1

Statement III alone is not sufficient.