Weird behaviour of NProbability

Question

n=19227;k=6018;Nx=10^6;

NProbability[0 < var < 200, 
 var \[Distributed] HypergeometricDistribution[n, k, Nx]]

(*0.000330001*)

N[CDF[HypergeometricDistribution[n, k, Nx], 200], 50]

(*0.99999999999980234474426879880990803313584713194835*)

I don't understand whats going on. I'm evaluating the CDF in both cases but NProbability is clearly giving me the wrong answer. What do I do?

Answer 1

By default, NProbability is using machine precision. This appears to be insufficient.

n = 19227; k = 6018; Nx = 10^6;

NProbability[0 < var < 200, 
var \[Distributed] HypergeometricDistribution[n, k, Nx], 
WorkingPrecision -> 100]


(* 0.9999999999996478278860752197394699718947902541813213958530809968591816102668832791282320631069752714 *)

Answer 2

The latest line should be

n = 19227; k = 6018; Nx = 10^6;
N[CDF[HypergeometricDistribution[n, k, Nx], 200], 100] - 
 N[CDF[HypergeometricDistribution[n, k, Nx], 1], 100]

0.99999999999980234474426879880990803313584713194819457153196994629316 38734132748161581793705151966009

See Wiki for info.