Chapter 5, Problem T5.10SPT

To determine

To find: The probability that detector B will go off.

Answer to Problem T5.10SPT

The probability is 0.75.

Explanation of Solution

Given:

Probability that detector will not go off is 0.35.

Probability that A will go off and B will not go off is 0.25

Calculation:

The probability that detector will go off is:

  $\begin{array}{c}P\left(\text{Detector A will go off}\right)=1-P\left(\text{Detector A will not go off}\right)\\ =1-0.35\\ =0.65\end{array}$

The probability that both A and B will go off is:

  $\begin{array}{c}P\left(\text{Detector A and B will go off}\right)=0.65-0.25\\ =0.40\end{array}$

The probability that detector B will go off is calculated as:

  $\begin{array}{c}P\left(\text{ B will go off}\right)=0.40+0.35\\ =0.75\end{array}$

Thus, the required probability is 0.75.

The correct option is (e).