What is the probability of drawing the marbles in description?

Question

A bag of marbles has 4 green, 6 blue and 9 red. If 4 marbles are drawn out of the bag without looking, what is the probability that there will be 3 red marbles and 1 blue marble?

Answer 1

The question should read, If 4 marbles are drawn out of the bag without replacement, what is the probability that you draw at random 3 red marbles and a blue marble?

For starters, let's name the variables to simplify the problem a bit:

G - green marble

B - blue marble

R - red mable

The bag looks like this with just the letters: GGGG BBBBBB RRRRRRRRR

So drawing each marble is an independent event and we can multiply each of the probabilities together:

P(3 red marbles and 1 blue)= (9/19)(8/18)(7/17)(6/16) = .0325