A bag contains 4 red marbles, 6 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?

Question

Make sure your answer is in fraction form.

Answer 1

Joshua's answer is completely correct.

You can, however, find the answer by a different method.

Use the hypergeometric distribution.

₄C₀ * ₆C₀ * ₅C₃ / ₁₅C₃ = 2/91

Answer 2

Hi Christian,

I'm assuming you are drawing without replacement. If so, use the multiplication rule. Probability of first marble being green is 5/15 or 1/3. You must subtract one green marble and one total marble to get the second probability since you already pulled one. That makes the second probability of a green 4/14. Finally, you subtract one from the green count and one from the total count to get the third probability, 3/13. Then, via Multiplication Rule:

P = (5/15) * (4/14) * (3/13)

Reducing:

P = (1/3) * (2/7) * (3/13)

P = 6/273

Reducing again:

P = 2/91

I hope this helps.