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

A. 7%

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) = (A \cap B)/(A) = (0.04)/(0.56) = 0.07`

So the correct answer is:

A. 7%