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.

Given: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.

What to do:To find the number of black balls in the bag.

Solution:

Let us say probability of getting a black ball is $P( A)$ and Probability of getting a white ball is $P( B)$.

Bag contains 15 white balls Lets say there are $x$ black balls

Total balls in the bag$=15+x$

Probability of drawing a black ball $=\frac{no.\ of\ black\ balls}{no.\ of\ total\ balls}=\frac{x}{x+15}$

Probability of drawing a white ball $=\frac{no.\ of\ white\ balls\ in\ the\ bag}{no.\ of\ total\ balls}=\frac{15}{x+15}$

Given that $P( A) =3P( B)$

$\frac{x}{x+15} =3\times \frac{15}{x+15}$

$\Rightarrow x=45$

No of black balls $=45$.