Question

A bag contains $3$ red balls and $5$ black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red?

Answer 1

Calculate the probability for the drawn ball is not red

The number of red balls, $n\left(R\right)=3$.

The number of black balls, $n\left(B\right)=5$.

So, the number of balls that are not red is $n\left(R\text{'}\right)=n\left(B\right)$.

$\Rightarrow n\left(R\text{'}\right)=5$

The number of total balls, $n\left(T\right)=n\left(R\right)+n\left(B\right)$

$$\begin{gathered} \Rightarrow n\left(T\right)=3+5 \\ \Rightarrow n\left(T\right)=8 \end{gathered}$$

Thus, the probability of getting a ball that is not red, $P\left(R\text{'}\right)=\frac{n\left(R\text{'}\right)}{n\left(T\right)}$.

$\Rightarrow P\left(R\text{'}\right)=\frac{5}{8}$.

Hence, the probability of getting a ball that is not red is $\frac{5}{8}$.