Question

1. 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

1. Out of all the positive results, what are the chances you get a false positive?

2. If given a negative result, what is the probability of getting a false negative?

3. If a child actually has the defect, what is the probability that the test shows a positive result?

4. What is the probability of a positive result from the total?

Answer 1

Total population under study = 1,000,000.

It is given that only 0.5% cases have defect.

So total population that have defect = 1000000*0.5/100 = 5000.

So in total 5000 people have this defect.

Now if the accuracy of the test 96%. Then total number of people who have defect and are shown positive in the test = 0.96*5000 = 4800.

So number of people who have the defect but have not got positive results = 5000-4800 = 200.

Number of people who don’t have the defect = 1000000-5000 = 995000

Number of people who dont have the defect and the teet correctly shows negative results=

0.96*995000 = 955200

Total number of people who don’t have the defect but their results falsely show positive results =

995000 - 955200 = 39800.

So the table will be

	Test shows positive	Test shows negative	Total
Has Defect	4800	200	5000
Does not have defect	39800	955200	995000
Total	44600	955400	1,000,000

A) Out of all positive results, probability of getting a false positive result = 39800 / 44600 = 0.89

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

C) If the child has a defect, Probability that the test shows positive result = 4800/5000 = 0.96

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