A bag contains 8 red marbles, 5 white marbles, and 6 blue marbles. You draw 4 marbles out at random, without replacement. Find the following probabilities and round to 4 decimal places.

Question

a. The probability that all the marbles are red is

b. The probability that none of the marbles are red is

Answer 1

prob(all 4 red) = (8/19)(7/18)(6/17)(5/16) = 35/1935
or
prob(all red) = C(8,4)/C(19,4) = 70/3876 = 35/1938

Prob(none red) = C(11,4)/C(19,4) = 330/3876 = 55/646
or
prob(none red) = (11/19)(10/18)(9/17)(8/16) = 55/646