Question

A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue?

Answer 1

Let 5 red pens be R₁ , R₂ , R₃ , R₄ , R₅ . 8 blue pens be B₁ , B₂ , B₃ , B₄ , B₅ , B₆ , B₇ , B₈ . and 3 green pens be G₁ , G₂ , G₃ . 

Sample space, 

S = {R₁ , R₂ , R₃ , R₄ , R₅, B₁ , B₂ , B₃ , B₄ , B₅ , B₆ , B₇ , B₈, G₁ , G₂ , G₃ } 

∴ n(S) = 16 

Let A be the event that Rutuja picks a blue pen. 

∴ A = {B₁ , B₂ , B₃ , B₄ , B₅ , B₆ , B₇ , B₈}

∴ n(A) = 8

∴ P(A) = \(\frac{n(A)}{n(S)}\)= 8/16

∴ P(A) = 1/2 

∴ The probability that Rutuja picks a blue pen is 1/2 .