Question

Red, blue, yellow, and green marbles are in a bag, with 14 marbles of each color. One white marble is added to the bag for a total of 57 marbles. If three marbles are chosen without replacement, what is the probability that all three marbles will be yellow?

a. 13/1,045
b. 728/61,731
c. 2,744/185,193

Answer 1

Option a: 13/1045

Explanation:

The yellow marbles are 14 in a total of 57 marbles. So we have that:

First marble being yellow: Probability = 14/57

Second marble being yellow: Probability = 13/56 (one yellow marble is already taken, so we have 13 in a total of 56)

Third marble being yellow: Probability = 12/55

Final probability: (14/57) * (13/56) * (12/55)

simplifying 14 with 56:

Final probability: (1/57) * (13/4) * (12/55)

simplifying 12 with 4:

Final probability: (1/57) * (13) * (3/55)

simplifying 3 with 57:

Final probability: (1/19) * (13) * (1/55) = 13 / 1045

Correct option: a.