Question

In a survey of a town, 56% of residents own a car, 21% of residents owns a truck, and 4% of residents own both a car and a truck. What is the conditional probability that a person who owns a car also owns a truck? A. 7% B. 17% C. 44% D. 19%

Answer 1

Answer:

A. 7%

Step-by-step explanation:

We build the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a resident owns a car.

B is the probability that a resident owns a truck.

We have that:

$A = a + (A \cap B)$

In which a is the probability that a resident has a car but not a truck and $A \cap B$ is the probability that a resident has both a car and a truck.

By the same logic, we have that:

$B = b + (A \cap B)$

4% of residents own both a car and a truck.

This means that $A \cap B = 0.04$

56% of residents own a car

This means that $A = 0.56$. So

$A = a + (A \cap B)$

$0.56 = a + 0.04$

$a = 0.52$

What is the conditional probability that a person who owns a car also owns a truck?

$P(B|A) = \frac{A \cap B}{A} = \frac{0.04}{0.56} = 0.07$

So the correct answer is:

A. 7%