Answer:
e) 0.14
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that a driver does not have a valid driver's license.
B is the probability that a driver does not have insurance.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a driver does not have a valid driver's license but has insurance and [tex]A \cap B[/tex] is the probability that a driver does not have any of these things.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
We start finding these values from the intersection.
4% have neither
This means that [tex](A \cap B) = 0.04[/tex]
6% of all drivers have no insurance
This means that [tex]B = 0.06[/tex]. So
[tex]B = b + (A \cap B)[/tex]
[tex]0.06 = b + 0.04[/tex]
[tex]b = 0.02[/tex]
12% of all drivers do not have a valid driver’s license
This means that [tex]A = 0.12[/tex]
So
[tex]A = a + (A \cap B)[/tex]
[tex]0.12 = a + 0.04[/tex]
[tex]a = 0.08[/tex]
The probability that a randomly selected driver either fails to have a valid license or fails to have insurance is about
[tex]P = a + b + (A \cap B) = 0.08 + 0.02 + 0.04 = 0.14[/tex]
So the correct answer is:
e) 0.14
