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

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

=
`(0.9504)/(0.9504+0.0008) \\=0.9992`