# A bag contains 4 white and 5 black balls.

Question:

A bag contains 4 white and 5 black balls. A ball is drawn at random from the bag. 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 r objects from given n objects is ${ }^{n} C_{r}$

Now, total no. of ways to pick a ball from 9 balls is ${ }^{9} \mathrm{C}_{1}=9$

Our desired output is to pick a white ball. So, no.of ways to pick a white ball from 4 white balls (because the white ball can be picked from only white balls) is ${ }^{4} \mathrm{c}_{1}=4$

Therefore, the probability of picking a white ball $=\frac{4}{9}$

Conclusion: Probability of picking a white ball from 4 white balls and 5 white balls is $\frac{4}{9}$