Question

A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball find the number of black balls in the bag. [CBSE 2017]

Answer 1

The number of white balls in a bag = 15.
Let the number of black balls in that bag be x.
Then, the total number of balls in bag = 15+x.

Now, P(black ball)=$\frac{x}{15+x}$and P(white ball)=$\frac{15}{15+x}$.
According to question, P(black ball) = 3 P(white ball)
$$\begin{gathered} \Rightarrow \frac{x}{15+x}=3\times \frac{15}{15+x} \\ \Rightarrow \frac{x}{15+x}=\frac{45}{15+x} \\ \Rightarrow x=45. \end{gathered}$$
Hence, number of black balls in bag = x = 45.