Question

A bag contains 6 red, 4 black and some white balls:

1. Find the number of white balls in the bag if the probability of drawing a white ball is `1/3`.
2. How many red balls should be removed from the bag for the probability of drawing a white ball to be `1/2`?

Answer 1

i. Red balls = 6, Black balls = 4, White balls = x

P (white ball) = `x/(10 + x) = 1/3`

`\implies` 3x = 10 + x

`\implies` x = 5 white balls

ii. Let y red balls be removed, black balls = 4, white balls = 5

P(white ballls) = `5/((6 - y) + 4 + 5) = 1/2`

`\implies 5/(15 - y) = 1/2` 

`\implies` 10 = 15 – y

`\implies` y = 5 white balls

So 5 balls should be removed.