5% of a population has a certain genetic condition. A test for this condition co
ID: 3260708 • Letter: 5
Question
5% of a population has a certain genetic condition. A test for this condition correctly detects it with
probability 0.99. However, the test indicates the condition is present in 15% of cases where it is
actually absent. Suppose a randomly select individual from the population is tested. Fine the
probability that
a) the individual has the genetic condition (G) and the test says they have it (T).
b) the individual does not have the condition and the test still says they have it.
c) the test indicates the condition is present.
d) the individual has the condition given that the test says they have it.
Explanation / Answer
Let us first tabulate the information. We will create a cross table and then we will calculate conditional probability.
Let us assume we have 10000 number of people in population (for ease of calculation).
Actual Records
Present
Absent
Total
Records Obtained Through Test
Present
495
1425
1920
Absent
5
8075
8080
Total
500 (5%)
9500
10000
Answer A ) This is straight forward .
495/10000 = 0.0495
Answer B)
1425/10000 = 0.1425
Answer C)
1920/10000 = 0.1920
Answer D)
495/1920 = 0.2578 (Conditional Probability)
Actual Records
Present
Absent
Total
Records Obtained Through Test
Present
495
1425
1920
Absent
5
8075
8080
Total
500 (5%)
9500
10000
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