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krok68 [10]
3 years ago
6

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.
Mathematics
1 answer:
Musya8 [376]3 years ago
7 0

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

   

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