Question

A rare birth defect occurs in approximately 0.5% of all cases in males. If we sample all the males born in 2019 in a specific region, fill out the chart below and answer the following questions. A test can be done with 96% accuracy to determine if a child has the birth defect.

Test shows Positive

Test Shows Negative

Total

Has Defect

Does Not have Defect

Total

1,000,000

Out of all the positive results, what are the chances you get a false positive?
If given a negative result, what is the probability of getting a false negative?
If a child actually has the defect, what is the probability that the test shows a positive result?
What is the probability of a positive result from the total?

Answer 1

A) of the positive tests the probability of obtaining a false positive result = 39800/44600 = 0.89

B) Probability of a false negative result, when the result is negative = 200/955400 = 0.00021

C) If the child is sick, the probability that the test will be positive = 4800/5000 = 0.96

D) Probability of a positive result of the total = 44600/1000000 = 0.0446.

Explanation:

Total study population = 1,000,000.

0.5% of patients are sick

So the total sick population = 1,000,000 * 0.5 / 100 = 5,000.

So, in total 5000 patients are sick

If the test is 96% accurate, with sick people and a positive test result = 0.96 * 5000 = 4800.

So the number of patients who are sick with a negative result = 5000-4800 = 200.

Number of healthy people = 1000000-5000 = 995000

Number of healthy people and that the test is negative =

0.96 * 995000 = 955200

Total number of healthy people but with false positive results false positives =

995000 - 955200 = 39800..