Question

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

Answer 1

We know,
P(getting red ball) = 1/4
P(getting blue ball) = 1/3
Let the no. of balls = x
Therefore, P(getting orange ball) = 10/x

We know,
P(getting red ball) + P(getting blue ball) + P(getting orange ball) = 1
⇒$\frac{1}{4}+\frac{1}{3}+\frac{10}{x}$ = 1
⇒ $\frac{10}{x}$ = 1 -$\frac{1}{4}$ -$\frac{1}{3}$
⇒ $\frac{10}{x}$= 1 - $\frac{7}{12}$
⇒ $\frac{10}{x}$ =$\frac{5}{12}$
⇒$10\times 12$ = $5\times x$
⇒x = 24

Therefore, the no. of balls = x
= 24