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 Rutuja picks a blue pen.

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

∴ n(A) = 8

∴ P(A) = `("n"("A"))/("n"("S")) = 8/16`

∴ P(A) = `1/2`

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