Chapter 15, Problem 14E

To determine

To find: the probability that she would end up paying more than $100 to repair the pollution control system.

Answer to Problem 14E

0.08

Explanation of Solution

Given:

  $P\left(F\right)=0.2$

  $P\left(E/F\right)=0.4$

Formula used:

  $P\left(E/F\right)=\frac{P\left(E\cap F\right)}{P\left(F\right)}$

Calculation:

F = car’s pollution control system is faulty

E = exceeds $100 to repair the system

  $\begin{array}{c}P\left(E\cap F\right)=P\left(E/F\right)\times P\left(F\right)\\ =\left(0.4\right)\left(0.2\right)\\ =0.08\end{array}$

Therefore 8% of cars pay more than $ 100 to repair control system.