Chapter 10.4, Problem 16E

To determine

Tocalculate:

The probability of the month on which company paid overtime wages and hired temporary help.

Answer to Problem 16E

The probability of the month on which company paid overtime wages and hired temporary help $0.17$ .

Explanation of Solution

Given information:

Paid overtime wages paid for $=9$ months

Overtime wages paid for $=7$ months

Temporary help hired for $=4$

Formula used:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

Calculation:

There are $12$ months in year. Assume that event $A$ denote wages were paid during $7$ months and event $B$ denote temporary help were hired during $4$ months.

It is further stated that during $9$ months completely paid overtime wages or hired temporary help.

Then, with the help of given information given probability as follows:

  $P\left(A\right)=\frac{7}{12},P\left(B\right)=\frac{4}{12},P\left(AorB\right)=\frac{9}{12}$

Then, the required probability of $A$ or $B$ is as given follows:

  $\begin{array}{l}P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)\\ \frac{9}{12}=\frac{7}{12}+\frac{4}{12}-P\left(AandB\right)\\ P\left(AandB\right)=\frac{7}{12}+\frac{4}{12}-\frac{9}{12}\\ =0.17\end{array}$

Hence, the answer is $0.17$ .

So, the probability of the month on which company paid overtime wages and hired temporary help $0.17$ .