Question

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?

Answer 1

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.