A diagnostic test for a disease D has two outcomesSolutionaP

A diagnostic test for a disease, D, has two outcomes

a)P( Test positive | Disease)

In this case, event A is the event you have this disease, and event B is the event that you test positive.

Here, P(B|A)=1

b)P( Test positive | No Disease)

Thus P(B|not A) is the probability of a \"false positive\": that you test positive even though you don\'t have the disease.

P(B|not A)=0.05

c)P( Test positive )

P(B|A)=1, P(A)=.001, and P(B) may be derived by conditioning on whether event A does or does not occur:

by baye\'s theorem

P(B)=P(B|A)P(A)+P(B|not A)P(not A)

=1*0.001+0.05*0.999

=0.05

d)P( Disease | Test Positive)

P(A|B)=P(A)P(B|A) / P(B)

0.001*1/0.05

=0.02