Question

A box contains a certain number of balls. Some of these balls are marked A, some are marked B and the remaining are marked C. When a ball is drawn at random from the box P(A) = `1/3` and P(B) = `1/4`. If there are 40 balls in the box which are marked C, find the number of balls in the box.

Answer 1

P(C) = 1 – [P(A) + P(B)]

= `1 - [1/3 + 1/4]`

= `1- 7/12`

= `5/12`

Probability = `"Number of favorable outcomes"/"Total number of all possible outcomes"`

Given that 40 balls in the box are marked C.

`=> 5/12 = 40/"Total number of all possible outcomes "`

`=>` Total number of all possible outcomes = `(40 xx 12)/5 = 96`

∴ The number of balls in the box is 96.