= P(E1|A)
By Bayes' theorem, we know that
P(E1|A) =
1
1
1
1
2
2
3
3
P(E )P(A|E )
P(E )P(A|E )+P(E )P(A|E )+P(E )P(A|E )
=
1 1
2
3
1
1
1
1
3
1
0
3
3
3
2
×
=
× + × + ×
Example 18 Suppose that the reliability of a HIV test is specified as follows:
Of people having HIV, 90% of the test detect the disease but 10% go undetected Of
people free of HIV, 99% of the test are judged HIV–ive but 1% are diagnosed as
showing HIV+ive From a large population of which only 0 1% have HIV, one person
is selected at random, given the HIV test, and the pathologist reports him/her as
HIV+ive