Question

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets,

i. a red balloon. 

ii. a blue balloon, 

iii. a green balloon.

Answer 1

Let the 2 red balloon be R₁ , R₂ , R₃ blue balloons be B₁ , B₂ , B₃ , and 4 green balloons be G₁ , G₂ , G₃. , G₄ . 

Sample space, 

S = {R₁ , R₂ , B₁ , B₂ , B₃ , G₁ , G₂ , G₃ , G₄ } 

∴ n(S) = 9 i. Let A be the event that Pranali gets a red balloon.

∴ A = { R₁, R₂}

∴ n(A) = 2

∴ P(A) = \(\frac{N(A)}{(n(S)}\)

∴ P(A) = 9/2

∴ The probability that Pranali gets a red balloon is 9/2.

ii. Let B be the event that Pranali gets a blue balloon.

∴ B = { B1, B2, B3}

∴ N(B) = 3

∴ P(B) = \(\frac{N(B)}{(n(S)}\) = 3/9

∴ P(B) = 1/3

∴ The probability that Pranali gets a blue balloon is 1/3. 

iii. Let C be the event that Pranali gets a green balloon.

∴ C = {G₁, G₂, G₃, G₄}

∴ n(C) = 4

∴ P(C) = \(\frac{N(C)}{(n(S)}\)

∴ P(C) = 9/4

∴ The probability that Pranali gets a green balloon is 9/4.