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?

A. 10 21 B. 11 21 C. 2 7 D. 5 7 Answer: Option A Explanation: Total number of balls = (2 + 3 + 2) = 7. Let S be the sample space. Then, n(S) = Number of ways of drawing 2 balls out of 7 = 7C2 ` = (7 x 6) (2 x 1) = 21. Let E = Event of drawing 2 balls, none of which is blue.  n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls. = 5C2 = (5 x 4) (2 x 1) = 10.  P(E) = n(E) = 10 . n(S) 21