Question

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that both the balls are of the same colour.

 

Answer 1

Out of 16 balls, two balls can be drawn in ¹⁶C₂ ways.
∴ Total number of elementary events = ¹⁶C₂ = 120

'Two balls drawn are of the same colour' means that both are either white or black or red.
 Out of seven white balls, two white balls can be drawn in ⁷C₂ ways.
 Similarly, two black balls can be drawn from five black balls in ⁵C₂ ways and two red balls can be drawn from four red balls in ⁴C₂ ways.
 Therefore, number of ways of drawing two balls of the same colour = ⁷C₂ + ⁵C₂ + ⁴C₂ = 21 + 10 + 6 = 37
i.e. favourable number of ways = 37
   Hence, required probability = \[\frac{37}{120}\]