Hey everybody,

I had the same issue… and in my oppinion the formular is not correct.

I also tried to reproduce the example down below, but without success.

Soop please let my explain myself:

We want the following probability:

`P(y matches at least one of the x_i) = 1-P(y matches none of the x_i)`

Now lets check a single probability (as shown in formular (4):

` P(y matches x) = fp(\theta)`

(fp(\theta) means the probabitity for a false positive)

According to that

`P(y does not match x) = 1 - fp(\theta)`

(I think we can assume that the matchings are independent) it follows:

`P(y matche none of the x_i) = [1 - fp(\theta)]^M`

Sooo in total we should have:

`P(y matches at least one of the x_i) = 1-P(y matches none of the x_i)`

` = 1 - [1 - fp(\theta)]^M`

I hope there is no mistake.

Well How I said I wanted to reproduce the results (with the result of fp_x(\theta) = 10^20).

Soo I wrote a simple code. And this code supported my caculations.

```
import scipy.special
n = 1024
w = 21
T = 14
M = 10
def false_positive(n, w, T):
return overlap_set(n, w, T) / capacity(n, w)
def capacity(n, w):
return scipy.special.binom(n, w)
def overlap_set(n, w, T):
return scipy.special.binom(w, T) * scipy.special.binom(n - w, w - T)
def false_positive_set(n, w, T, M):
return 1 - (false_positive(n, w, T))** M
def false_positive_set_alternative(n, w, T, M):
return 1 - (1 - false_positive(n, w, T))** M
print(false_positive_set(n, w, T, M))
print(false_positive_set_alternative(n,w,T,M))
```

Please, correct me if I am wrong. But I think you can even see that in the (wrong) formular itself:

If the prob. for false positives is super small and the calculate `^M`

the number gets even smaller.

And finally we have a super small number, close to zero, and then subtracting that from 1. So the result of formular (9) has to be close to 1.

Well, I hope I could express myself. Please correct me if I am wrong.

Or give me some other feedback to that.

Thank you all very much (and merry christmas )