probability question for the season

I found the answer to the following probability question very interesting. Let me know your answer so that we could all be mathematically prepared for the season :)

Suppose a certain flu test is 99% sensitive and 99% specific, that is, the test will correctly identify a flu patient as testing positive 99% of the time, and will correctly identify a non-user as testing negative 99% of the time. This would seem to be a relatively accurate test. Let's assume a school decides to test its students for flu, and 0.5% of the students has flu. We want to know the probability that, given a positive flu test, a student is actually a flu patient. Let "Y" be the event of being a flu patient and "N" indicate being a non-patient. Let "+" be the event of a positive flu test. We need to know the following:
P(Y), or the probability that the student is a flu patient, regardless of any other information. This is 0.005, since 0.5% of the students are flu patients. This is the prior probability of Y.
P(N), or the probability that the student is not a flu patient. This is 1 8722; P(Y), or 0.995.
P(+|Y), or the probability that the test is positive, given that the student is a flu patient. This is 0.99, since the test is 99% accurate.
P(+|N), or the probability that the test is positive, given that the student is not a flu patient. This is 0.01, since the test will produce a false positive for 1% of non-users.
P(+), or the probability of a positive test event, regardless of other information. This is 0.0149 or 1.49%, which is found by adding the probability that a true positive result will appear (= 99% x 0.5% = 0.495%) plus the probability that a false positive will appear (= 1% x 99.5% = 0.995%). This is the prior probability of +.
Given this information, what is the posterior probability P(D|+) of an student who tested positive actually being a flu patient?

(a) P > 80%
(b) 40% (c) 10% (b) P

所有跟帖： 

• C -haha2000- ♂ (0 bytes) () 04/29/2009 postreply 19:09:53

• answer -praisethelord- ♂ (393 bytes) () 04/30/2009 postreply 10:41:13

• great. I am waken up by you. -戲雨飛鷹- ♀ (0 bytes) () 04/30/2009 postreply 11:08:35