A common test for AIDS is called the ELISA test Among 100000

A common test for AIDS is called the ELISA test. Among 1,000,000 people who are given the ELISA test, we can expect results similar to those given in the table.                                                                     

A1: Test Positive     B1:Carry AIDS Virus= 4885   B2:Do not carry: 73,630  Totals: 78515

A2: Test Negative B1:Carry AIDS Virus= 115   B2:Do not carry:921,370 Totals: 921,485

Totals    B1:Carry AIDS Virus= 5,000 B2:Do not carry: 995,000  Totals: 1,000,000  

If one of these 1,000,000 people is selected randomly, find the following probabilities:

a) P(B1) (i.e. probability carry the AIDS virus)

b) P(A1) (i.e. probability person tests positive)

c) P(A1 l B2) (i.e. probability person tests postive given they do not carry)

d) P(B1 l A1) (i.e. probability person carries given they test positive)                

Solution

a.) P(B1) = 5000/1000000 = 0.005

b.) P(A1) = 78515/1000000 = 0.078515

c.) P(A1|B2) = 73630/995000 = 0.074

d.) P(B1|A1) = 4885/78515 = 0.06222