Chapter 5.3, Problem 104E

To determine

To find:the percentage of calls results in a contribution.

Answer to Problem 104E

  $\left(c\right)0.02$

Explanation of Solution

Given:

  $\begin{array}{l}P\left(\text{Test }A\text{positive}\right)=0.9\\ P\left(\text{Test }B\text{positive}\right)=0.8\end{array}$ .

Calculation:

The complement rule is $P\left(A^c\right)=P\left(\text{not }A\right)=1-P\left(A\right)$

Apply the complement rule:

  $\begin{array}{l}P\left(\text{Test }A\text{negative}\right)=1-P\left(\text{Test }A\text{positive}\right)=1-0.9=0.1\\ P\left(\text{Test }B\text{negative}\right)=1-P\left(\text{Test }B\text{positive}\right)=1-0.8=0.2\end{array}$

According to the question the two test operates independently from each other, thus it can use the multiplication rule for independents event:

Add the corresponding probabilities:

  $\begin{array}{l}P\left(\text{Neither test positive}\right)=P\left(\text{Both test negative}\right)\\ =P\left(\text{Test }A\text{negative}\right)\times P\left(\text{Test }B\text{negative}\right)\\ =0.1\times 0.2=0.02\end{array}$

Thus, according to the option, the correct option is $\left(c\right)0.02$ .