>>11831495disease affects 1% of the population.
The test for it is 99% accurate.
You test positive.
What is the chance you are actually infected?
ROUND #1
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100000 people tested
1% are sick = 1000 people
99% are healthy = 99000 people
test accuracy 99%
of the 1000 sick, 990 will test as positive
of the 1000 sick, 10 will test as negative (FN)
of the 99000 healthy, 9990 will test as positive (FP)
of the 99000 healthy, 89010 will test as negative
990/(990+9990)=0.090163934
testing positive means you have a 9% chance of being sick
so, send the positives to a new round of testing
note: 10 sick people get a false negative, if asymptomatic then will spread the disease
ROUND #2
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990+9990=10980 people tested
9% are sick = 990 people
91% are healthy = 9980 people
test accuracy 99%
of the 990 sick, 980 will test as positive
of the 990 sick, 10 will test as negative (FN)
of the 9980 healthy, 100 will test as positive (FP)
of the 9980 healthy, 9880 will test as negative
980/(980+100)=0,907407407
testing positive means you have a 91% chance of being sick
so, send the positives to a new round of testing
note: 10 sick people get a false negative, if asymptomatic then will spread the disease
ROUND #3
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980+100=1080 people tested
91% are sick = 983 people
9% are healthy = 97 people
test accuracy 99%
of the 983 sick, 973 will test as positive
of the 983 sick, 10 will test as negative (FN)
of the 97 healthy, 1 will test as positive (FP)
of the 97 healthy, 96 will test as negative
973/(973+1)=0.998973306
testing positive means you have a 99.9% chance of being sick
note: 10 sick people get a false negative, if asymptomatic then will spread the disease
