Consider a test for using a particular drug. The test will produce 99% true positive results for drug users and 99% true negative results for non-drug users. Suppose that 0.5% of people are users of the drug. What is the probability that a randomly selected individual with a positive test is a drug user?

Step-by-step explanation:

Using  Bayes' theorem, we have:

is a conditional probability: the likelihood of event A occurring, given that B is true.

is also a conditional probability: the likelihood of event B occurring, given that A is true.

P(A) and P(B) are the marginal probabilities of observing A and B, independently of each other.

We solve thus:

                 =

                 =

                 =

                 =

                 = or %

Therefore, if an individual tests positive, it is more likely than not (1 - 33.2% = 66.8%) that they do not use the drug.

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