Chapter 13.10, Problem 4CYU

To determine

The probability of picking a purple or the number $2$ is to be estimated.

Answer to Problem 4CYU

The probability is $\frac{2}{5}$ .

Explanation of Solution

Given:

  

Concept Used:

Probability of an event is calculated as:

  $P=\frac{n\left(E\right)}{n\left(S\right)}$

Where,

The probability of an event: $P$

The number of favourable outcomes: $n\left(E\right)$

The total number of events in the sample space: $n\left(S\right)$

Calculation:

The probability of purple ball is calculated as:

  $\begin{array}{l}P\left(A\right)=\frac{n\left(P\right)}{n\left(S\right)}\\ P\left(A\right)=\frac{1}{5}\end{array}$

The probability of ball of number $2$ is calculated as:

  $\begin{array}{l}P\left(B\right)=\frac{n\left(2\right)}{n\left(S\right)}\\ P\left(B\right)=\frac{1}{5}\end{array}$

So, the probability of picking a purple or the number $2$ is given as:

  $\begin{array}{l}P=P\left(A\right)+P\left(B\right)\\ P=\frac{1}{5}+\frac{1}{5}\\ P=\frac{2}{5}\end{array}$

Conclusion:

Hence, the probability of picking a purple or the number $2$ is $P=\frac{2}{5}$ .