A bag contains 3 red, 3 white and 3 green balls. One ball is taken out

1.	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» 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

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»

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

Discussion

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