Chapter 10, Problem 9CR

To determine

To calculate:

Probability of employee works both part time and $5$ days each week.

Answer to Problem 9CR

Probability of employee works both part time and $5$ days each week is $0.02$ .

Explanation of Solution

Given information:

Total no of employee work in company $=100$

Total no of employee works either both part time and $5$ days each week $=92$

Total no of employee works part time $=14$

Total no of employee works $5$ days each week $=80$

Let’s, assume event $A$ denote employees who works part time, event $B$ denote employees who work $5$ days a week.

So,

  $\begin{array}{l}P\left(A\right)=\frac{14}{100}\\ P\left(B\right)=\frac{80}{100}\\ P\left(AorB\right)=\frac{92}{100}\end{array}$

The required probability is,

  $\begin{array}{l}P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)\\ P\left(AandB\right)=\frac{14}{100}+\frac{80}{100}-\frac{92}{100}\\ P\left(AandB\right)=0.02\end{array}$

Hence, Probability of employee works both part time and $5$ days each week is $0.02$ .