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