Question

There are 6 brown, 5 blue, and 2 orange marbles in a hat. What is the probability of picking two orange marbles in a row without returning the marbles back to the hat? (Write your answer as a fraction.)

Answer 1

The correct answer is 1/78.

Explanation:
There are 2 orange marbles out of 13 total marbles, so the probability of your first marble being orange is 2/13.

After this one is drawn, since it is not returned, the probability of getting a second orange marble is 1/12, since there is only 1 orange marble left out of 12 total marbles.

This gives us the total probability 2/13(1/12)=2/156=1/78.