Quick Notes

A box contains \(8\) green balls, \(12\) black balls and a number of white balls.

A white ball is chosen at random from the box.

The probability of getting a white ball is \(\dfrac{3}{7}\)​.

What is the number of white balls in the box?

Let \(w\) be the number of white balls.

Then,

\(\begin{aligned}n(S)&=8+12+w\\\\&=20+w.\\\\\end{aligned}\)

So,

\(\begin{aligned} P(w)&=\dfrac{n(w)}{n(S)} \\\\\dfrac{3}{7}&=\dfrac{w}{20+w} \\\\3(20+w)&=7(w) \\\\60+3w&=7w \\\\4w&=60 \\\\w&=15.\\\\ \end{aligned}\)

Thus, the number of white balls in the box is \(15\).