disease with 80% accuracy. The test is also not perfect in terms of detecting a
ID: 3277091 • Letter: D
Question
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? (d) What is the intuition for the two results?Explanation / Answer
Answer:
a)
From the given information, table is made for 100 persons.
sick
not sick
positive
0.8
0.096
0.896
negative
0.2
98.904
99.104
1
99
100
Table in terms of Probabilities.
sick
not sick
positive
0.008
0.00096
0.00896
negative
0.002
0.98904
0.99104
0.01
0.99
1
b).
P =0.8/0.896
=0.892857
c).
P =0.00096/0.896
= 0.001071
d).
The test is good at detecting a sick person (89.3%) and 0.1% wrongly diagnosing a not sick person as positive.
sick
not sick
positive
0.8
0.096
0.896
negative
0.2
98.904
99.104
1
99
100
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