Suppose I have a population, $P$, of 100 individuals and I am devising 3 algorithmic methods to sample 20 people from said population: $A$, $B$, and $C$. We know that $C$ is a random, unbiased algorithm.
Suppose the outputs for each algorithm are 100-length lists of 0's and 1's. Binary data where a 1 indicated that an individual is selected for a sample. There are 20 1's in each list:
$A(P)$ = $[0, 1, 0, 1, ... , 1]$
$B(P)$ = $[1, 0, 1, 1, ... , 0]$
$C(P)$ = $[1, 0, 0, 1, ... , 1]$
If I know that C is random, but I suspect that $A$ is not random and that $B$ is random, how can I go about testing this? I initially tried McNemar's test due to having paired nominal data. But then realized the statistic would always be 0 since my each list contains exactly 20 1's. Is Fisher's Exact test the best test for this type of experiment? How can I test a suspicion that $B$ is likely random (or similar to $C$) and show that the opposite is true for $A$?