Why is the last equation (463/500)^2 if its either one or 2 happening? Isnt that equation only the probability that 2 happens?
Can you send an image or a reminder of the question. We don’t have it in-front of us!
The probability that any one ELISA gives a positive result on an HIV-negative sample is 37/500. Therefore, the probability it gives a negative result on such a sample is 463/500.
Here we are using the complement rule: P(1 or 2 positives out of 2) = 1 - P(no positives)
P(no positives) = (463/500)^2 since the tests are independent.
Dang, it’s a double complement rule! 
