Suppose you have the following information. 12% of all drivers do not have a valid driver’s license, 6% of all drivers have no insurance, and 4% have neither (i. e., do not have driver’s license and do not have insurance). The probability that a randomly selected driver either fails to have a valid license or fails to have insurance is about

(a) 0.18

(b) 0.2

(c) 0.22

(d) 0.072

(e) 0.14

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:

In which a is the probability that a driver does not have a valid driver's license but has insurance and is the probability that a driver does not have any of these things.

By the same logic, we have that:

We start finding these values from the intersection.

4% have neither

This means that

6% of all drivers have no insurance

This means that . So

12% of all drivers do not have a valid driver’s license

This means that

So

The probability that a randomly selected driver either fails to have a valid license or fails to have insurance is about

So the correct answer is:

e) 0.14

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18