Probability of dependent events

Question

A bag of 10 marbles: 3 are green, 2 are red, and 5 are blue. A marble is chosen at random, and without putting it back, another one is chosen at random. What is the probability that the first is red and the second is blue? Write the dragon in the simplest form.

Answer 1

There are 10 total marbles in the beginning, and 2 of those are red, so the probability of drawing a red one is:

2:10, or 1:5.

Now there are only 9 total marbles, and 5 of those are blue, so the probability of drawing a blue one is:

5:9.