2- used to detect the virus in a person is positive 80% of the time when the per

Question

2- used to detect the virus in a person is positive 80% of the time when the person virus and 5% of the time when the person does not have the virus. Let A be the event"the Reliability of Testing. A certain virus infects one in every 200 people. A test has the person is infected" and B be the event "the person tests positive." Using Bayes' Theorem, when a person tests positive, determine the probability that the person is infected Using Bayes' Theorem, when a person tests negative, determine the probability that a person is not infected 4- 5- t it for use on

Explanation / Answer

Question

Pr(Infection) = 1/200 = P(A)

P(Ac) = 199/200

Pr(Test is positive l Person has the virus) = 0.80

Pr(B l A) = 0.80

Pr(Test is positve l person dont have the virus) = 0.05

Pr(B l Ac) = 0.05

Pr(Bc l Ac) = 0.95

4 - Pr(Person is infected l test positve) = Pr(A l B) = Pr(B l A) * P(A)/ [Pr(B l A) * P(A) + Pr(B l Ac) * P(Ac)]

= [0.80 * 1/200] / [0.80 *1/200 + 0.05 * 199/200]

= 0.004/ 0.05375 = 0.0744

5- Pr(Person is not infected l Tested negative) = Pr(Ac l Bc ) = Pr(Bc l Ac) * P(Ac)/ [Pr(Bc l Ac) * P(Ac) + Pr(Bc l A) * P(A)]

= (0.95 * 199/200)/ (0.95 * 199/200 + 0.20 * 1/200)

= 0.9989

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