Question

The probability of selecting a red ball at random from the jar that contains only red, blue and orange balls is `1/4`. The probability of selecting a blue ball at random from the same jar is `1/3`. If the jar contains 10 orange balls, find the total number of balls in the jar.

Answer 1

It is given that,

P(getting a red ball) =`1/4`  and P(getting a blue ball) =`1/3`

Let P(getting an orange ball) be x.

Since, there are only 3 types of balls in the jar, the sum of probabilities of all the three balls must be 1.

`therefore  1/4 + 1/3 + x = 1`

`rArr x = 1 - 1/4 -1/3`

`rArr x = (12-3-4)/12`

`rArr x = 5/12`

∴ P(getting an orange ball) =`5/12` 

Let the total number of balls in the jar be n.

∴ P(getting an orange ball) = `10/n`

`rArr 10/n = 5/12`

`rArr n = 24`

Thus, the total number of balls in the jar is 24.