A bag contains 8 red marbles, 4 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn
will be red?

At the start, there are a total of 19 marbles. The chance of pulling one red is 8/19 (because there are 8 red).

Based on the way you stated the questions, I do not assume the red marble that was pulled first would be put back, so there’s only 18 marbles left to choose from and 7 of those are red. So on the second marble, you have 7/18 chance of pulling a red.

Again, since neither of the first two marbles were put back, you now have 17 marbles left and 6 of those are red. So you have a 6/17 chance of pulling a third red marble.

Multiply those together, 8/19 * 7/18 * 6/17 and you’ll have your answer.