A jar contains 10 blue marbles 5 red marbles 4 green marbles

A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement).

(a) What is the probability that one will be green and the other red?

(b) What is the probability that one will be blue and the other yellow?

Solution

(a) What is the probability that one will be green and the other red?
   Chosen Marbles are green and other red = 5 C 1 * 4 C 1 / 20 C 2 = (5 * 4) * 2 / (20 * 19) = 0.1052

(b) What is the probability that one will be blue and the other yellow?
   Chosen Marbles are blue and other yellow = 10 C 1 * 1 C 1 / 20 C 2 = (10 * 1) * 2 / (20 * 19) = 0.05263