The probability of selecting a red ball at random from a 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 in the jar.

Options

A. `21`
B. `22`
C. `23`
D. `24`

Answer

D

Explanation

P(getting a red ball) = ` 1/4`, P(getting a blue ball) = `1/3`.
Let P(getting an orange ball ) be x.
Since there are only thre types of balls in the jar, the sum of probabilities of drawing these balls must be 1.
` :. 1/4 + 1/3 + x = 1 rArr 7/12 + x = 1 rArr x = (1-7/12) = 5/12`.
` :.` P(getting an orange ball) = ` 5/12`. ....(i)
Let the total number of balls in the jar be n.
Number of orange balls = 10.
` :. ` P(getting an orange ball ) ` = 10/n`.
` rArr 10/n = 5/12 rArr 5n = 120 rArr n = 24 ` [using (i)].
Hence, the total number of balls in the jar is 24.