Question

A bag contains 5 white balls and some blue balls. If the probability of drawing a blue ball is double that of a white ball, determine the number of blue balls in the bag

Answer 1

Let the number of blue balls be x.

Number of white balls = 5

∴ Total number of balls = (x + 5)

P(blue ball is drawn) = `x/(x + 5)`

P(white ball is drawn) = `5/(x + 5)`

According to the given condition, the probability of drawing a blue ball is double that of a white ball.

∴ P(blue ball is drawn) = 2 × P(white ball is drawn)

∴ `x/(x +5) = 2 xx 5/(x + 5)`

∴ x(x + 5) = 10(x + 5)

∴ x² + 5x = 10x + 50

∴ x² – 5x – 50 = 0

∴ x² – 10x + 5x – 50 = 0

∴ x(x – 10) + 5(x – 10) = 0

∴ (x – 10)(x + 5) = 0

∴ x – 10 = 0 or x + 5 = 0

∴ x = 10 or x = – 5

But, number of balls cannot be negative.

∴ x = 10

∴ The number of blue balls in the bag is 10.