Question

A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball; find the number of black balls in the box.

Answer 1

Number of white balls in the bag = 30

Let the number of black balls in the box be x.

∴ Total number of balls = x + 30

P(drawing a black ball) = `x/(x + 30)`

P(drawing a white ball) = `30/(x + 30)`

It is given that, `P("drawing a black ball") = 2/5 xx P("drawing a white ball")`

⇒ `x/(x + 30) = 2/5 xx 30/(x + 30)`

⇒ `x/(x + 30) = 12/(x + 30)`

⇒ x² + 30x = 12x + 360

⇒ x² + 18x – 360 = 0 

⇒ x² + 30x – 12x – 360 = 0

⇒ x(x + 30) – 12(x + 30) = 0

⇒ (x + 30)(x – 12) = 0

⇒ x = –30 or x = 12

Since number of balls cannot be negative, we reject x = –30

⇒ x = 12

Therefore, number of black balls in the box is 12.