Question

A bag contains $5$ white balls, $7$red balls, $4$ black balls and $2$ blue balls. One ball is drawn at random from a bag. What is the probability that ball drawn is neither white nor black?

Answer 1

Step 1 Determining the probability:

Given that a bag contains $5$ white balls, $7$red balls, $4$ black balls and $2$ blue balls.

So, the total number of outcomes $=5+7+4+2=18$

We have to find the probability of getting neither a white nor black ball.

So, the total number of favorable outcomes $=Red+Blue=7+2$

The formula for probability is

$$\begin{gathered} Probabilty=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes} \\ \Rightarrow P\left(neitherwhitenorblack\right)=\frac{9}{18} \\ \therefore P\left(neitherwhitenorblack\right)=\frac{1}{2} \end{gathered}$$

Hence, the probability of getting neither a white nor black ball is $\frac{1}{2}$.