SOLUTION: A virus has a positivity rate of 4/10000. A school has 2000 students. What is the probability that at least one of these 2000 students tests positive?
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Question 1166510: A virus has a positivity rate of 4/10000. A school has 2000 students. What is the probability that at least one of these 2000 students tests positive?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability that at least one student tests positive is equal to 1 minus the probability that no student tests positive. In general, the probability of any given number of positives could NOT be calculated using the binomial distribution because the events are not independent, i.e. the probability that student A tests positive is dependent on the disease status of the students that interact with that student. But since we are actually calculating the probability that no one is positive, we can get away with using the stated positivity rate.
\ =\ {{n}\choose{r}}\,(p)^r\,(1-p)^{n-r})
\ =\ {{2000}\choose{0}}\,\(0.0004\)^0\,\cdot\,\(0.9996\)^{2000}\ =\ 1\,\cdot\,1\,\cdot\(0.9996\)^{2000}\ \approx\ 0.45)
So the probability of at least one is approximately 
John
My calculator said it, I believe it, that settles it
I > Ø
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