Question

In: Statistics and Probability

One in a thousand people are afflicted with the dreaded zigma disease. A pharmaceutical company develops...

One in a thousand people are afflicted with the dreaded zigma disease. A pharmaceutical company develops a test for this disease and brags that only 5% of those with the disease test negative for it and 1% of those who do not have zigma will test positive for it.

What is the probability that a person who tests positive actually has zigma?

  1. 9.99%

  2. 1.09%

  3. 8.68%

  4. 5.01%

  5. 9.51%

Solutions

Expert Solution

P(having the disease) = 0.001

P(tests negative | have the disease) = 0.05

P(tests positive | don't have the disease) = 0.01

P(tests positive | have the disease) = 1 - P(tests negative | have the disease) = 1 - 0.05 = 0.95

P(tests positive) = P(tests positive | have the disease) * P(have the disease) + P(tests positive | don't have the disease) * P(don't have the disease)

                          = 0.95 * 0.001 + 0.01 * (1 - 0.001)

                          = 0.01094

P(have the disease | tests positive) = P(tests positive | have the disease) * P(have the disease) / P(tests positive)

                                                         = 0.95 * 0.001 / 0.01094

                                                         = 0.0868

                                                         = 8.68% (ans)

orchestra answered 2 years ago
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