Accepting 13% of the population being black (as cited above), then having zero of 20 nominees being black has a probability of 6.2% only slightly less than the 7.1% chance of having 5 or more black nominees as occurred in 2004 and 2006. (Zero happened 3 times out of 15 according to Robert163’s post.)
But it seems to me that 13% of the US population being black is not particularly relevant. What fraction of actors and actresses are black, or what fraction of leading and supporting roles are performed by black actors? If that’s more like the 5% membership in the Academy, then you’d expect to come up with zero nominations of 20 nominations in 36% of the years, and you should get 5 or more in less than 0.05% of the years.
Even at a much larger percentage of Blacks eligibles, it’s still not unusual to see what has occurred. If Blacks filled 10% of the roles (rather than 13%), then you’d see no nominees 12% of the time and five or more 3% of the time.
I don’t take the cited numbers alone as satisfying even a preponderance of the evidence criterion.