Solution:
Population in the city= 10,000
As genetic condition affects 8% of the population.
8 % of 10,000
[tex]=\frac{8}{100}\times 10,000=800[/tex]
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 [tex]=\frac{1}{100}\times 800=8[/tex]
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 [tex]=\frac{1}{100}\times 9200=92[/tex]
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
[tex]=\frac{\text{1 percent of 9200}}{9200}\\\\ \frac{\frac{1}{100}\times 9200}{9200}=\frac{92}{9200}\\\\ =0.01[/tex]
that is Probability equal to 0.01 or 1%.
