Answer to Question #192953 in Statistics and Probability for oxman

Question

Because a new medical procedure has been shown to be effective in the early detection of an illness, a medical screening of the population has been proposed. The probability that the test correctly identifies someone with the illness as positive is 0.99, and the probability that the test correctly identifies someone without the illness as negative is 0.95. The incidence of the illness in the general population is 0.0001.

Hint: You may use a probability diagram or tree diagram to aid you in solving the problem.

Let D= Presence of the disease in the population

A= absence of the disease in the population

N= Negative results

P= positive results

a. What is the probability that the test will diagnose a person as having the illness? [4]

b. You take the test, and the result is positive. What is the probability that you have the illness?

Answer 1

a

the probability that the test will show a positive result is the sum of the probabilities that you are sick and determined correctly and the probability that you are healthy but the test was wrong

$P=(1-0.0001)*(1-0.95)+0.0001*0.99=0.050094$

b

the probability that you are sick despite the fact that the test showed a positive result is you are sick and the correct divided sum of probabilities is determined that you are sick and it is determined correctly and the probability that you are healthy but the test was wrong

$P=0.0001*0.99/((1-0.0001)*(1-0.95)+0.0001*0.99)\approx0.00197$