Question

(12 points) In Africa, the Joint United Nations Programme on HIV/AIDS determined that the probability that an individual adult in Africa has the disease is 0.05. Assume for any HIV test, the probability that the test result is positive given a real HIV carrier is 0.98, and the probability that the test result is positive given a healthy individual (i.e., a person who does not carry HIV virus) is 0.05. (a) (5 pts) What is the probability that a test result will be negative

Answer 1

90.35% probability that a test result will be negative

Explanation:

We have these following probabilities:

0.05 = 5% probability that an individual adult has the disease.

If the adult has the disease, 1 - 0.98 = 0.02 = 2% probability of a negative test.

1 - 0.05 = 0.95 = 95% probability that an individual adult does not have the disease.

If the adult does not have the disease, 1 - 0.05 = 0.95 = 95% probability of a negative test.

What is the probability that a test result will be negative

2% of 5% or 95% of 95%. So

p = 0.02*0.05 + 0.95*0.95 = 0.9035

90.35% probability that a test result will be negative