A bag has 4 red marbles, 5 white marbles, 6 blue marbles, and 7 green marbles. Three marbles are drawn from the bag (without replacement). What is the probability that they are all the same color?
Four different cases
P( all red ) = 4 / 22 * 3/21 * 2/20 = 1/385
P( all white) = 5/22 * 4/21*3/20 = 1/154
P( all blue) = 6/22 * 5/21 * 4/20 = 1/77
P(all green) = 7/22 * 6/21 * 5/20 = 1/44
Total probability = 1/385 + 1/154 + 1/77 + 1/44 = 69 / 1540 ≈ 4.5%
