Question

A box contains some black balls and $30$ white balls. If the probability of drawing a black ball is two-fifths of the probability of drawing a white ball, find the number of black balls in the box.

Answer 1

Let the number of black balls be $x$, then,

Total number of balls $=30+x$

Thus, the probability of black balls $=\frac{x}{30+x}$

and the probability of white balls $=\frac{30}{30+x}$

Given: Probability of black ball $=\frac{2}{5}\times$ probability of white ball

$\frac{x}{30+x}=\frac{2}{5}\times \frac{30}{x+30}$

$5x=60$

$x=12$

Hence, the number of black balls $=12$.