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 0.92. Of the disease is not actually​ present, the probability of a positive test result​ (indicating that the disease is​ present) is 0.01. a. If 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

Answer 1

Answer: 0.74

Explanation:

A= "The person is sick "

B= "The test gives a positive result"

P(A)=0.03

P(B|A)=0.92

P(B|A')=0.01

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

P(B)=P(B|A)P(A)+P(B|A')P(A')=0.92*0.03+0.01*0.97=0.0373

Based in Bayes Rule

P(A|B)=P(B|A)P(A)/P(B)=0.92*0.03/0.0373=0.74