Question 1112713
Out of {{{"10,000"}}} people, {{{0.05*"10,000"=500}}} have the disease.
Of those, {{{0.98*500}}} test positive, and start looking for treatment.
The other {{{(1-0.98)*500=0.02*500=10}}} test negative,
and do not think they have the disease, but they do.
 
Out of the same {{{"10,000"}}} people, another {{{"10,000"-500="9,500"}}} people do not have the disease.
However, among them, {{{0.02*"9,500"=190}}} test positive, and worry unnecessarily.
The remaining {{{"9,500"-190="9,310"}}} people without the disease test negative.
 
Out of the whole {{{"10,000"}}} people,
there are {{{10+"9,310"="9,320"}}} people who have tested negative.
Out of those who tested negative, the fraction without the disease is
{{{"9,310"/"9,320"=about}}}{{{highlight(0.9989)}}} .
That is the probability that a person who tests negative does not have the disease.