Question

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

Answer 1

Let the number of blue balls be x.

Number of red balls = 5

Total number of balls = x + 5

P (getting a red ball) =  5/(x+5)

P (getting a blue ball) = x/(x+5)

Given that,

`2(5/(x+5)) = x/(x+5)`

10(x+5) = x² + 5x

x² - 5x- 50 = 0

x(x-10) + 5(x-10) = 0

(x-10)(x+5) = 0

Either x - 10 =0 or x +5 = 0

x = 10 or x = -5

However, the number of balls cannot be negative.

Hence, number of blue balls = 10