Acertain genetic condition affects 8% of the population in a city of 10,000. suppose there is a test for the condition that has an error rate of 1% (i. e., 1% false negatives and 1% false positives).

consider the values that would complete the table below.

has condition does not have condition totals

test positive

test negative

totals

what is the probability (as a percentage) that a person has the condition if he or she tests positive? (round your answer to one decimal place.)

Solution:

Population in the city= 10,000

As genetic condition affects 8% of the population.

8 % of 10,000

As, it is also given that, there is an error rate of 1% for condition (i.e., 1% false negatives and 1% false positives).

So, 1% false negatives means out of 800 tested who are found affected , means there are chances that 1% who was found affected are not affected at all.

So, 1% of 800

Also,  1% false positives means out of 10,000 tested,[10,000-800= 9200] who are found not affected , means there are chances that 1% who was found not affected can be affected also.

So, 1% of 9200

1. Has condition Does not have condition totals  = 800

2. Test positive =92

3. Test negative =8

4. Total =800 +92 +8=900

5. Probability (as a percentage) that a person has the condition if he or she tests positive= As 8% are found positive among 10,000 means 9200 are not found affected.But there are chances that out of 9200 , 1% may be affected

that is Probability equal to 0.01 or 1%.

so, converting firstly the mixed fractions to improper fractions and then "adding".