A certain disease affects about 1 out of 10, 000 people. There is a test to check

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A certain disease affects about 1 out of 10, 000 people. There is a test to check whether the person has the disease. The test is quite accurate. In particular, we know that

  • The probability that the test result is positive (suggesting the person has the disease), given that the person does not have the disease, is only 2 percent;
  • The probability that the test result is negative (suggesting the person does not have the disease), given that the person has the disease, is only 1 percent.

A random person gets tested for the disease and the result comes back positive. What is the probability that the person has the disease?

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