Question

thirty - five percent of cars that are inspected have faulty pollution control systems. the cost of repairing a pollution control system exceeds $150 about 30% of the time. when a driver takes his car in for inspection, what is the probability that he will end up paying more than $150 to repair the pollution control system?
the probability is
(type an integer or a decimal. do not round )

Explanation:

Step1: Identify relevant probabilities

Let $A$ be the event that a car has a faulty pollution - control system and $B$ be the event that the repair cost exceeds $150$. We are given $P(A)=0.35$ and $P(B|A) = 0.3$.

Step2: Use the multiplication rule of probability

The multiplication rule for conditional probability is $P(A\cap B)=P(B|A)P(A)$.
Substitute the given values: $P(A\cap B)=0.3\times0.35$.
$P(A\cap B)=0.105$

Answer:

$0.105$