Chapter 4, Problem 1RWYL

Whistle Blowers Although there is legal protectionfor “whistle blowers”—employees who report illegalor unethical activities in the workplace—it has beenreported that approximately 23% of those who reportedfraud suffered reprisals such as demotion or poor performanceratings. Suppose the probability that an employeewill fail to report a case of fraud is .69. Find the probabilitythat an employee who observes a case of fraudwill report it and will subsequently suffer some form ofreprisal.

To determine

The probability that a employee will report a fraud and subsequently suffer with some form of reprisal.

Answer to Problem 1RWYL

$0.0713$

Explanation of Solution

Given:

Approximately 23% those who reported fraud, suffer with form of reprisal.

69% will fail to report a fraud.

Formula Used:

For any two independent events $A$ and B, probability of occurring both the events is

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

Probability of not occurring an event A is given by

$P\left(A^c\right)=1-P\left(A\right)$

Calculation:

Let $A$ be the event that suffers with a form of reprisal.

$\begin{array}{c}P\left(A\right)=\frac{23}{100}\\ =0.23\end{array}$

Let $B$ be the event that the employee will fail to report a fraud.

$\begin{array}{c}P\left(B\right)=\frac{69}{100}\\ =0.69\end{array}$

Therefore, $B^c$ be the event that the employee will report a fraud.

$\begin{array}{c}P\left(B^c\right)=1-P\left(B\right)\\ =1-0.69\\ =0.31\end{array}$

As $A\text{and}{B}^c$ are independent events,

$\begin{array}{c}P\left(A\text{and}{B}^c\right)=P\left(A\right)\cdot P\left(B^c\right)\\ =0.23\times 0.31\\ =0.0713\end{array}$

Hence, the probability that a employee will report a fraud and subsequently suffer with some form of reprisal is $0.0713$.