Consider a fictious virus that causes one to become a zombie! There is a test for...
Consider a fictious virus that causes one to become a zombie! There is a test for this disease with the following sensitivity and specificity:
sensitivity : P(+|zombie virus) = 0.99
specificity : P(−|no zombie virus) = 0.9
The virus can be detected before one turns into a zombie, which takes a week or so, but there is no cure.
At any given time, the proportion of people that have contracted the virus is given by P(Zombie) = 0.001.
Suppose that you have been given a positive test for the virus, what is the probability that you are actually infected?
Show work please.
Homework Answers
P(Actually infected | positive test for virus)
A = actually infected
B = positive test for virus
P(A|B)
= P(A and B)/P(B)
P(A and B) = P(B|A)P(A) = 0.99 * 0.001
P(B) = P(B|A)P(A) + P(B|A')P(A')
= 0.99 * 0.001 + (1 - 0.9) ( 1 - 0.001)
= 0.10089
hence
required probability = 0.99* 0.001/ 0.10089
= 0.0098126
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