I don’t understand equation 9 in SDR chapter of the BAMI book:
My expectation of what equation 9 is supposed to calculate is that if for example we have a list of SDRs, X, with only two elements x1 and x2, then equation 9 is supposed to calculate the probability that a random SDR y will match any of the SDRs in X.
This means that we should calculate:
Probability false positive between x1 and y + Probability false positive between x2 and y
But from the way equation 9 is written, it looks to me that it is calculating:
Probability of no false positive between x1 and y + Probability of no false positive between x2 and y
Can someone please explain the intuition behind equation 9 and illustrate how it works using a small example?