A bag contains 10 marbles: 2 are green, 6 are red, and 2 are blue. Omar chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles he chooses are green? Write your answer as a fraction in simplest form.
There are a total of 10 marbles in the bag, so the probability of choosing one green marble at random is 2/10 or 1/5. After one marble is chosen, there will be 9 marbles left in the bag, including only 1 green marble. So the probability of choosing another green marble is now 1/9.
To find the probability of both events happening, we multiply the probabilities:
1/5 x 1/9 = 1/45
Therefore, the probability of Omar choosing two green marbles is 1/45.