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?
There are a total of 15 marbles in the bag. To find the probability that all three marbles drawn will be green, we need to find the total number of ways to draw three marbles out of the bag and the number of ways to draw three green marbles.
The total number of ways to draw three marbles out of 15 is:
15C3 = (15!)/(3!12!) = 455
This means there are 455 different combinations of three marbles that can be drawn out of the bag.
The number of ways to draw three green marbles out of 5 is:
5C3 = (5!)/(3!2!) = 10
This means there are only 10 different combinations of three green marbles that can be drawn out of the bag.
Therefore, the probability of drawing three green marbles is:
10/455 = 2/91
So the exact probability that all three marbles drawn will be green is 2/91.