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.