listen up, mathletes:
A certain virus affects one in every 200 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) If a person tests positive, what is the probability that the person is infected?
(b) If a person tests negative, what is the probablity that the person is negative?
the answer key in the back of my textbook gives the answer to (a) as 0.074 and the answer to (b) as 0.999 but it gives no clue to the process i should use to arrive at these numbers.
i am in need of help. anyone writing to me with the answer, "ask mischka" should not write at all in the first place. he doesn't know either.
PS: bonus: mischka came through with Bayes's theorem which goes like this except i can't write in math & in html at the same time, so deal:
P(A|B) = [P(A) � P(B|A)] / {[P(A) � P(B|A)] + [P(A') � P(B|A')]}
so there.
