I was really hoping somebody better qualified would jump in on this one....
A) You're choosing four of the twenty. There are C(20,4) ways to choose four of twenty.
You want to make sure that, of the eight red, you pick zero. There are C(8,0) ways to do this.
You want to make sure that, of the other twelve you pick some random four. There are C(12,4) ways to do this.
Then the probability of picking four, none of which is red, should (I believe) be:. . . . .
...or about 0.1021671827..., or about 10.2%.
B) Um.... Lemme get back to you on this....