Suppose that six percent of the people in the world have a particular genetic defect and that a screening test is 89 percent accurate for people who have it and 76 percent accurate for people who do not.
If 1,810 people are screened for the defect, which is the best prediction for the number of people with the defect who are identified as having it?
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Let the event GD be 'has genetic defect' and let the event TP be 'tests positive'. Using conditional probability we can write:
P(TP|GD) = 0.89
P(GD) = 0.06
\[\large P(GD \cap TP) = P(GD) \times P(TP|GD)=0.06\times0.89\]
Now multiply 1,810 by the probability of the intersection of 'has genetic defect' and 'test positive'. Round the result to the nearest integer to predict the number of people with the defect who are identified as having it.