Question

A bag contains 5 red marbles, 6 blue marbles and 4 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that all three marbles drawn will be blue?

Answer 1

4.4%

Explanation:

The overall probability is the product of the individual probabilities.

Total number of marbles: 15

Original number of blue marbles: 6

First drawing (6 blue and 15 total):

p(blue) = 6/15 = 2/5

Second drawing (5 blue and 14 total):

p(blue) = 5/14

Third drawing (4 blue and 13 total):

p(blue) = 4/13

p(blue followed by blue followed by blue) = 2/5 × 5/14 × 4/13 = 40/910 = 4/91

p(blue followed by blue followed by blue) = 4/91 = 0.043956... = 4.4%