An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is the probability that both the balls are red?

Step-by-step solution

Total number of balls in the urn = 10 + 5 = 15 Number of ways to draw 2 balls from 15 balls = ¹⁵C₂ Number of ways to draw 2 red balls from 5 red balls = ⁵C₂ Required probability = ⁵C₂ ¹⁵C₂ ⁵C₂ = 5 4 2 = 10 ¹⁵C₂ = 15 14 2 = 105 Required probability = 10 105 = 2 21