A container holds 3 blue marbles, 4 red marbles, 6 green marbles, and 2 yellow marbles. If two marbles are drawn at random, what is the probability that both selected marbles are either blue or yellow?

Explanation

There are 15 marbles in total: 3 blue, 4 red, 6 green, and 2 yellow. The probability of drawing two blue marbles is C(3,2)/C(15,2) = (3*2)/(15*14) = 1/35. The probability of picking two yellow marbles is C(2,2)/C(15,2) = (2*1)/(15*14) = 1/105. The probability of selecting one blue and one yellow marble is (C(3,1)*C(2,1))/C(15,2) = (3*2)/(15*14) = 2/35. Adding these probabilities: 1/35 + 1/105 + 2/35 = 2/21. Hence, the probability that both marbles are either blue or yellow is 2/21.