91Ó°ÊÓ

The probability of any event is defined as the ratio of the number of outcomes associated with the event to the total number of possible outcomes.

The formula for probability of any event E is $\mathit{P}\mathbf{=}\frac{\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{s}\mathbf{}\mathbf{f}\mathbf{a}\mathbf{v}\mathbf{o}\mathbf{r}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{t}\mathbf{o}\mathbf{}\mathbf{E}}{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{s}}$.

In a container, there are 2 white, 3 black, and 4 red balls.

The total number of outcomes possible is same as the total number of balls present in the container.

Find the total number of outcomes by adding the number of balls.

2+3+4=9

There are 3 black balls, this implies that the number of outcomes favourable are 3 and total number of outcomes are 9.

Apply the formula for probability, that is $P=\frac{numberofoutcomesfavorabletoE}{totalnumberofoutcomes}$ to get the required probability.

$P=\frac{3}{9}=\frac{1}{3}$

Hence the desired probability is $\frac{1}{3}$.

The ball selected should not be red implies that the ball must be either white or black, thus, the number of favorable outcome is sum of number of black and white ball.

Find the number of favorable outcome.

$2+3=5$

This implies that the number of outcomes favorable are 5 and total number of outcomes are 9.

Apply the formula for probability, that is $P=\frac{numberofoutcomesfavorabletoE}{totalnumberofoutcomes}$to get the required probability.

$P=\frac{5}{9}$

Hence the desired probability is $\frac{5}{9}$.