# An urn contains 9 red, 7 white, and 4 black balls.

Question:

An urn contains 9 red, 7 white, and 4 black balls. A ball is drawn at random. Find the probability that the ball is drawn is white

Solution:

We know that,

Probability of occurrence of an event

$=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$

By permutation and combination, total no.of ways to pick $\mathrm{r}$ objects from given $\mathrm{n}$ objects is ${ }^{n} C_{r}$

Now, total no. of ways to pick a ball from 20 balls is ${ }^{20} \mathrm{C}_{1}=20$

Our desired output is to pick a white ball. So, no.of ways to pick a white ball from 7 white balls(because the white ball can be picked from only white balls) is ${ }^{7} \mathrm{C}_{1}=7$

Therefore, the probability of picking a white ball $=\frac{7}{20}$

Conclusion: Probability of picking a white ball from 9 red,

7 white and 4 black balls is $\frac{7}{20}$