## Simple Probability

13.4  Simple Probability

 Example 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 $$15$$.