Question

A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 5% of the time if the person does not have the virus. (This 5% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".

a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A|B)=____ %

b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A'|B'). Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A'|B') =____ %

Answer 1

17300 289/300 P(has vines) = 11300 P (does not have vious) Has visus P (positive Test). Bolioo 97 P ( Negative Test) = 1 - 800 20/100 ( PC has vires positive Test) P (positive 4 has visus P (positive Test) Doesn't have vious P (positive Test) = 8/100 (Negative Test) Test) = -5/100 > 95/100 v 90 100 Lun? 300 30 000 P (positive & has vious) = P(posi tive Test ) = 300 1 299 + x so loo 100 300 = + 80 30,000 1495 30,000 1575 30,000 P(has visus/ positive Test) 80 0-0507% 30,000 1575 30,000

6 P(doesn't have vines / Negative Test) » P(Negative & does not have viores) P (Negative Test) 95 299 100 300 95 X 299 100 300 300 28405 30,000 28425 30,000 -9992960), Š 1.00%