(2) A disease happens in 1% of the population. There is a test that give us a po

Question

(2) A disease happens in 1% of the population. There is a test that give us a positive if a person has the disease with 80% accuracy. The test is also not perfect in terms of detecting a disease that is not there: 9.6% of the tests detect a disease when a person is not sick. (a) Make a table that shows in the rows, the possible resuts of the test (positive, negative) and in the columns the possibilities for a health status of a person (sick, not sick). Indicate in the respective cell the probability of that event. For example, mark in the appropriate cell the probability of getting a positive if you are sick (b) What is the probability of being being sick if your test was positive? (c) What is the probability of being not being sick if your test was positive?

Explanation / Answer

P (Sick)=0.01

P (Not Sick)=1-0.01=0.99

a)

b)

P(Sick|Positive)= P(Postive|Sick)*P(Sick)/P(Positive|Not Sick)*P(Not Sick)+P(Positive|Sick)*P(Sick)

= 0.8*0.01/(0.096*0.99+0.8*0.01)

= 0.0088

c)

P(Not sick|Positive)= 1-0.0088

= 0.9912

Sick Not sick Total Positive 0.8 0.096 0.896 Negative 0.2 0.904 1.104 Total 1 1 2

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