A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Explanation
Probability = 5C2/7C2 = 10/21
Total number of balls = 2 + 3 + 2 = 7
∴ Number of ways of drawing 2 balls out of 7 = 7C2 = (7 × 6) / (2 × 1) = 42/2 = 21
Number of balls other than blue = 5
∴ Number of ways of drawing 2 balls out of 5 = 5C2 = (5 × 4) / (2 × 1) = 20/2 = 10
∴ Required Probability = 10/21