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 \(15\).
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