Question

A bag contains 3 red, 3 white, 3 green, and 3 black balls. One ball is picked up from the bag at random. What is the probability that the ball drawn is:

a. white

b. not white. 

Answer 1

Let three red balls are R₁ ,R₂ ,R₃ 

Three White balls are W₁, W₂, W₃ 

Three green balls G₁, G₂,G₃ 

Three black balls B₁, B₂, B₃

S = {R₁ ,R₂ ,R₃ , W₁, W₂, W₃ , G₁, G₂,G₃ , B₁, B₂, B₃}

n(S) = 12

(a) Let A be the set of white balls

A = {W₁, W₂, W₃}

n(A) = 3

P(A) = `("n"("A"))/("n"("S")) = 3/12 = 1/4`

(b) Let B be the set of not white balls.

B = {R₁ ,R₂ ,R₃ ,G₁, G₂,G₃ , B₁, B₂, B₃}

n(B) = 9

P(A) =`("n"("B"))/("n"("S")) = 9/12 = 3/4`