5% of a population has a certain genetic condition. A test for this condition co

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

Suppose total population = 10,000

Population having genetic condition = 500

Test detects 0.99*500 = 495 cases.

Test detects the condition in 15% of cases where it is absent = 1500 cases

Note: TP denotes Test is Positive and TN denotes Test is Negative. GC denotes Genetic Condition & NC denoted No Condition

a.) P(GC & TP) = 495/10000 = 0.0495

b.) P(NC & TP) = 1500/10000 = 0.15

c.) P(TP) = 495 + 1500 = 1995/10000 = 0.1995

d.) P(GC given TP) = 495/1995 = 0.2481

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