Question

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

Answer 1

Steps: 2 Marks
Answer: 1 Mark

Let the number of black balls be $x$
Then total balls $=x+30$
P (black balls) $=\frac{x}{x+30}$
P(white balls) $=\frac{30}{x+30}$
But $\frac{x}{x+30}=\frac{2}{5}\times \frac{30}{x+30}$
$\Rightarrow 5x=60\Rightarrow x=12$
$\therefore$ Number of black balls $=12$.