Sebastian has a bag of 15 blue marbles, 18 red marbles, and 12 yellow marbles. He reaches into the bag three times and pulls out 2 red marbles and a blue marble. What is the probability that he reaches into the bag and pulls out a yellow marble next? A. 1/4 B. 8/21 C. 2/7 D. 5/14

Explanation:

Initially there are 15+18+12 = 45 marbles total. He selects 3 marbles (2 reds, 1 blue).

Assuming he doesn't put the three marbles back, this means there are now 45-3 = 42 marbles overall. The yellow count hasn't changed since the first three marbles do not involve yellow. We have 12 yellow out of 42 which leads to the fraction 12/42 to represent the probability of getting yellow.

Reduce 12/42 to get 2/7. You divide both parts by the GCF 6.

Side note: if he did put the marbles back, then the probability of getting yellow would be 12/45 = 4/15