Question

A new drug test needs to be evaluated. The probability of a random person taking drugs is 4%. The drug test tested positive for a person not taking drugs 2% of the time. The drug test tested negative for a person taking drugs 1% of the time. a. What is the probability that a random person tests negative? b. What is the probability that a person who tests negative is without any drug problems?

Answer 1

Answer:

Step-by-step explanation:

Given that a new drug test needs to be evaluated. The probability of a random person taking drugs is 4%.

The drug test tested positive for a person not taking drugs 2% of the time. The drug test tested negative for a person taking drugs 1% of the time.

                          Tested positive     Tested negative       Total

Having drug               0.98                        0.02                  1.00

not hav drug               0.01                        0.99                   1.00

a)            the probability that a random person tests negative

= Prob ( really negative and test negative) + Prob (positive and test negative)

$= 0.96*0.99+0.04*0.02= 0.9504+0.0008=0.9512$

b) the probability that a person who tests negative is without any drug problems

= $\frac{0.9504}{0.9504+0.0008} \\=0.9992$