A bag contains 3 red marbles, 7 blue marbles and 8 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?
First, we need to find the total number of ways to draw three marbles out of the bag. This can be calculated using combinations:
(total number of marbles) choose (number of marbles to draw)
= (3 + 7 + 8) choose 3
= 18 choose 3
= 816
Next, we need to find the number of ways to draw three green marbles out of the bag. This can be calculated using combinations as well:
(number of green marbles) choose (number of green marbles to draw)
= 8 choose 3
= 56
Therefore, the probability of drawing three green marbles is:
56/816
= 7/102
So the exact probability of drawing three green marbles out of the bag is 7/102.