Respuesta :
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:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a resident has a car but not a truck and [tex]A \cap B[/tex] is the probability that a resident has both a car and a truck.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
4% of residents own both a car and a truck.
This means that [tex]A \cap B = 0.04[/tex]
56% of residents own a car
This means that [tex]A = 0.56[/tex]. So
[tex]A = a + (A \cap B)[/tex]
[tex]0.56 = a + 0.04[/tex]
[tex]a = 0.52[/tex]
What is the conditional probability that a person who owns a car also owns a truck?
[tex]P(B|A) = \frac{A \cap B}{A} = \frac{0.04}{0.56} = 0.07[/tex]
So the correct answer is:
A. 7%
