A bag contains 10 marbles 4 are green 4 are red and 2 are blue. Donna chooses a marble at random, doesn't put it back, chooses another one at random. What’s the probability that both marbles are blue?

Answer 1

These 2 events are dependent on each other, which means the second event relies on what happened in the first pulling of marbles by Donna.

To start with there is 2 blue in 10 so that means there is a 2/10 or 1/5 chance that Donna pulls a blue.

The next time you pull there is 1 blue left with only 9 marbles remaining, since Donna pulled a blue one already). That means there is a 1/9 chance that Donna pulls a blue.

To get the combined chances all you do is multiply 1/5 by 1/9 which gives you a 1/45 chance of pulling 2 blue marbles in a row.