Question

The probability that a person has a certain disease is 0.03

Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.92

If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.02

a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present?

b. If the medical diagnostic test has given a negative result (indicating that the disease is not present), what is the probability that the disease is not present?

Answer #1

**Answer:**

a)

Given,

P(T+) = P(D)*P(T+|D) + P(D')*P(T+|D')

substitute values

= 0.03*0.92 + 0.97*0.02

= 0.0276 + 0.0194

= 0.047

P(D|T+) = P(D)*P(T+|D) / [P(D)*P(T+|D) + P(D')*P(T+|D')

substitute values

= 0.03*0.92 / (0.03*0.92 + 0.97*0.02)

= 0.0276 / (0.0276 + 0.0194)

= 0.0276 / 0.047

= 0.5872

b)

P(T-) = P(D')*P(T-|D') + P(D)*P(T-|D)

substitute values

= 0.97*0.98 + 0.03*0.08

= 0.953

P(D'|T-) = P(D')*P(T-|D') / P(D')*P(T-|D') + P(D)*P(T-|D)

substitute values

= 0.97*0.98 / (0.97*0.98 + 0.03*0.08)

= 0.9506 / 0.9506 + 0.0024)

= 0.9975

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