The probability problem needs clarification. Were the 8 baby chicks picked from a large (virtually infinite) litter of chicks that were stochastically sexed (Demming process control type) at a rate of 95% hens?

Open (virtually infinite) sets have different probabilities than closed (choosing from a set of which is 95% hens – sexing operation 100% accurate) In this case, the set you are selecting from has to have more than 100 chicks because 6 are roosters, but your sexing showed 5 out of 100 as roosters.

For the first, you have 5 out of 100 (20) raised to the 6th power multiplied by 95 out of 100 (1.0526315) raised to the 2nd power, divided by the number of ways you can select 2 of one kind and 6 of another out of 8 (# of combinations).

Crap.. my calculator does not have a factorial button. longhand time…

Ok.. the odds of getting a group of 6 roosters followed by 2 hens from a pull of an infinite group of chicks is 1 out of 1108033.24099…

There are 28 different ways you can get 6 roosters and 2 hens from a pull of 8 chicks.. meaning that odds of getting 6 roosters and 2 hens from an endless pile of little clucks sexed at 95% hen is 1 out of 39572.6157