Chapter 9.7, Problem 50E

To determine

To find: the probability that three people chosen at random would prefer flexible work hours.

Answer to Problem 50E

  $0.47$

Explanation of Solution

Given:

People which choose flexible work hour = 78%

People which choose rigid work hour = 13%

People which don’t know = 9%

Concept Used:

Let A and B be two independent events, then

  $P\left(A\text{ and }B\right)=P\left(A\right)\times P\left(B\right)$

Let E be the event that three people chosen at random would prefer flexible work hours

Let A be the event that both a person chosen at random would prefer flexible work hours.

Then,

  $\begin{array}{c}P\left(A\right)=78\%\\ =0.78\end{array}$

Here, choosing three persons at random and their opinion about work hours are independent events as choice of one individual doesn’t effect the choice of other one. And so, the probability of each choosing flexible work hour is 0.78.

So, the probability that three people chosen at random would prefer flexible work hours is:

  $\begin{array}{c}P\left(E\right)=0.78\times \text{0}\text{.78}\times \text{0}\text{.78}\\ =0.47\end{array}$