Question

Suppose there was a cancer diagnostic test was 95% accurate both on those that do and those do not have the disease. If 0.4% of the population have cancer, compute the probability that a tested person has cancer given that his test result indicates.

Answer 1

Complete Question

Suppose there was a cancer diagnostic test was 95% accurate both on those that do and 90% on  those do not have the disease. If 0.4% of the population have cancer, compute the probability that a particular individual has cancer, given that the test indicates he or she has cancer.

Answer:

The probability is  $P(C | A) = 0.0042$

Step-by-step explanation:

From the question we are told that

The probability that the test was accurate given that the person has cancer is  

      $P(A | C) = 0.95$

The probability that the test was accurate given that the person  do not have cancer is  

      $P(A | C') = 0.90$

The probability that a person  has  cancer is  

      $P(C) = 0.004$

Generally the probability that a person do not have cancer is  

       $P(C') = 1- P(C)$

=>    $P(C') = 1- 0.004$

=>    $P(C') = 0.996$

Generally the  probability that a particular individual has cancer, given that the test indicates he or she has cancer is according to  Bayes's theorem evaluated as

     $P(C | A) = \frac{P(A | C) * P(C)}{P(A|C) * P(C) + P(A| C') * P(C')}$

=>  $P(C | A) = \frac{ 0.95 * 0.004 }{ 0.95 * 0.004 + 0.90 * 0.996}$

=>  $P(C | A) = 0.0042$