Chapter 10.5, Problem 48E

To determine

To calculate:

The probability of the working on weekend.

Answer to Problem 48E

The probability of the working on weekend is $0.05$ .

Explanation of Solution

Given information:

Total evenings you work $=5$

Randomly assigned evenings $=5$

Total possibilities $=7$

Formula used:

Expression for combination

  ${}_n{C}_r=\frac{n!}{\left(n-r\right)!\cdot r!}$

Where,

  $n=$ objects

  $r=$ time

Calculation:

First, write the number of possible outcomes as the number of combinations of $7$ possibilities taken $2$ at a time, ${}_7{C}_2$ because the order is not important.

So, apply the expression for combination for $n$ objects taken $r$ at a time is as follows:

  ${}_n{C}_r=\frac{n!}{\left(n-r\right)!\cdot r!}$

The required number of combinations are as follows:

  $\begin{array}{l}{}_7{C}_2=\frac{7!}{\left(7-2\right)!\cdot 2!}\\ =\frac{7!}{5!\cdot 2!}\\ =\frac{7\cdot 6\cdot 5!}{5!\cdot 2\cdot 1}\\ =21\end{array}$

Now, find the number of favorable outcomes. Only one of the possible outcomes include not working on weekend.

So, the probability is as follows:

  $\begin{array}{l}P\left(notworkingonweekend\right)=\frac{1}{21}\\ =0.05\end{array}$

Hence, the probability of the working on weekend is $0.05$ .