Question

twenty - five percent of cars that are inspected have faulty pollution control systems. the cost of repairing a pollution control system exceeds $125 about 40% of the time. when a driver takes his car in for inspection, what is the probability that he will end up paying more than $125 to repair the pollution control system?
the probability is
(type an integer or a decimal. do not round.)

Explanation:

Step1: Define the probabilities

Let $P(F)$ be the probability of a car having a faulty pollution - control system. $P(F)=0.25$. Let $P(C > 125|F)$ be the probability that the cost of repair exceeds $125$ given that the pollution - control system is faulty. $P(C > 125|F)=0.4$.

Step2: Use the multiplication rule of probability

The multiplication rule for conditional probability is $P(A\cap B)=P(B|A)P(A)$. Here, we want to find $P(\text{faulty and cost}> 125)$. Let $A$ be the event that the pollution - control system is faulty and $B$ be the event that the cost of repair exceeds $125$. Then $P(A\cap B)=P(C > 125|F)P(F)$.
Substitute the given values: $P(C > 125|F)P(F)=0.4\times0.25$.
$0.4\times0.25 = 0.1$

Answer:

$0.1$