Can you please help me with this question?

Question

There are 6 blue and 9 red marbles in a bag. Three marbles are picked at random. What is the probability (%) of picking 2 blue and 1 red marble?

Answer 1

Assuming we are sampling without replacement:

There are three ways you can pick 2 blues and 1 red from the bag

BBR

BRB

RBB

Probability of BBR = 6/15 * 5/14 * 9/13 = 0.0989

Probability of BRB = 6/15 * 9/14 * 5/13 = 0.0989

Probability of RBB = 9/15 * 6/14 * 5/13 = 0.0989

Probability of any of those three occurring is 3 * 0.0989 = 0.2967

Answer 2

Three ways to get two blue and one red:

BBR or BRB or RBB

BBR = (6/15)(5/14)(9/13) = 9/91

BRB = (6/15)(9/14)(5/13) = 9/91

RBB = (9/15)(6/14)(5/13) = 9/91

Probability of 2B and 1R = 3(9/91)

Probability of 2B and 1R = 27/91

Probability of 2B and 1R ~ .2967