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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?

Correct Answer: 10 21

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


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