Question

The probability that a person has a certain disease is 0.03. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.9. If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.02.a) Suppose that the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present?b) What is the probability of a positive test result?

Answer 1

Answer:

a) 0.58

b) 0.0464

Step-by-step explanation:

A= The person is sick

B= The give a positive result

P(A)=0.03

P(A')=1-P(A)=1-0.03=0.97

P(B|A)=0.9

P(B|A')=0.02

P(B)=P(B|A)P(A)+P(B|A')P(A')=0.9*0.03+0.02*0.97=0.0464

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}=\frac{0.9*0.03}{0.0464}=0.58$