Disjoint subsets

Probability that 2 k-sized independent subsets A,B from set of size n are disjoint

Set size n:     #trials of each k=1,⌊n/2⌋:

k (A∩B=∅) n-kCk/nCk=

Try:
n=10 #trials=1000 

Probability that two k-sized subsets A,B are disjoint is n-kCk / nCk

n=10
k n-kCk   / nCk
1 9C1= 9 /  10 = .9
2 8C2=28 /  45 = .622
3 7C3=35 / 120 = .292
4 6C4=15 / 210 = .071
5 5C5= 1 / 252 = .004



An element of an n-set is in half (2n-1) of all (2n) subsets.
So the probability that it is in a randomly chosen subset is ½.

So the probability that it is in two randomly chosen subsets is 1/4.
and the probability that it is in neither of the two subsets is 3/4.
Same for each of the n elements, thus the probability that two subsets
are disjoint is (3/4)n.