Question

A diagnostic test for a disease is such that it (correctly) detects the disease in 99% of the individuals who actually have the disease. Also, if a person does not have the disease, the test will report that he or she does not have it with probability .99. Only 0.1% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that he/she has the disease, what is the conditional probability that he/she does, in fact, have the disease?

Answer 1

0.0901

Step-by-step explanation:

Let us assume 100 people have disease in the question

which is 0.1% of the total population. therefore, total population will be 100000.

now 99.9% of the population does not have the disease which is 100000-100= 99900.

from 100 people diseased people, 99 test positive, and 1 negative.

and from the 99900 of the non diseased people, 999 will be diagnosed diseased and 99900-999= 98,901 will be diagnosed non diseased

so, total number of people tested positive are 99+999= 1098

out of these many people only 99 people actually of the disease

what is the conditional probability that he/she does, in fact, have the disease=

99/1098= 0.0901