Question

A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is:

i. red. 

ii. not red. 

iii. either red or white.

Answer 1

Let the three red balls be R₁, R₂, R₃, three white balls be W₁, W₂, W₃ and three green balls be G₁ , G₂ , G₃ . 

Sample space,

S = {R₁, R₂, R₃, W₁, W₂, W₃,G₁ , G₂ , G₃} 

∴ n(S) = 9 

i. Let A be the event that the ball drawn is red. 

∴ A = {R₁ , R₂ , R₃ } 

∴ n(A) = 3

∴ P(A) = \(\frac{n(A)}{n(S)}\) = 3/9 

∴ P(A) = 1/3

ii. Let B be the event that the ball drawn is not red. 

B = {W₁,W₂,W₃,G₁,G₂,G₃} 

∴ n(B) = 6

∴ P(B) = \(\frac{n(B)}{n(S)}\) = 6/9

∴ P(B) = 2/3

iii. Let C be the event that the ball drawn is red or white.

∴ C = {R₁, R₂, R₃ ,W₁, W₂, W₃ } 

∴ n(C) = 6

∴ P(C) = \(\frac{n(C)}{n(S)}\) = 6/9

∴ P(C) = 2/3

∴ P(A) = 1/3; ∴ P(B) = 2/3; ∴ P(C) = 2/3