999
P(A|E) = P(Person tested as HIV+ive given that he/she
is actually having HIV)
= 90% 
90
0 9
 100
 
and
P(A|E′) = P(Person tested as HIV +ive given that he/she
is actually not having HIV)
= 1% = 1
100 = 0 01
Now, by Bayes' theorem
P(E|A) =
P(E)P(A|E)
P(E)P(A|E)+P(E )P(A|E )
 
 
=
0 001 0