Plot Probability Curve with Summation
In your formula, wouldn't it be the product instead of the sum? Anyways, my original thought was to use the Poisson distribution, but that wouldn't work since it's without replacement. The problem is that the factorial function is only defined for whole numbers, so you'd need to use the gamma function.
I have the following problem:
I'm working on a formula to calculate some network effects. The idea is that I have 450 "red users" and 6550 "blue users" which sums up to 7000 users in total. Now I would like to plot "picking x users (the same user cannot be picked twice, so this is sampling without replacement) and calculate the probability that at least 1 user is red". 
E.g for x = 3, that means I'm picking 3 random users out of 7000 and check if any of these are "red users"
The probability for having at least 1 red user is p = 1 - the probability all 3 picks are blue users and the probability for a blue user is equal to p = 6550/7000, right? 
Resulting in a probability for at least 1 red user:
* p = 1 - 6550/7000 * 6549/6999 * 6548/6998 *
Therefore i came up with the formula:
f(x) = e^-(1- sum of (6500-i)/(7000-i)); for i = 0, till x)
What I've realized is that the curve is pretty edgy since it's just going from a value in ℕ to the next value in ℕ. 
Although adding decimal numbers wouldn't make that much sense since "picking 0,5 users or even 0,01 users" is just stupid, I would like to see the full graph in order to be able to compare the formula to some others. 
Is there any way I can implement this in python?
Best regards,
Korbi