Question

A hospital is trying to understand the effectiveness of a test in diagnosing a disease. The following are facts about the disease and the test.

P(having disease) = .08

P(NOT having disease) = .92

P(negative test | NOT having disease ) = .87

P(positive test | having disease ) = .90

What is Pr(NOT having disease AND positive test)?

What is Pr(having disease | positive test)?

What is Pr(NOT having disease | negative test)?

Answer 1

Given:

P(Having disease) = 0.08

P(Not having disease) = 0.92

P(Negative test | Not having disease) = 0.87

P(Positive test | having disease) = 0.90

P(Positive test and having disease) = P(Positive test | having disease)*P(Having disease)

= 0.90 * 0.08

P(Positive test and having disease) = 0.072

P(Not having disease and negative) = P(Negative test | Not having disease)*P(Not having disease)

= 0.87 * 0.92

P(Not having disease and negative) =  0.8004

1)

P(Not having disease and positive test) = P(Not having disease) - P(Not having disease and negative)

= 0.92 - 0.8004

P(Not having disease and positive test) = 0.1196

2)

3)

P(Not having disease | Negative test) = 0.990103909