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?

Question:
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