A jar contains seven blue marbles and four red marbles. Suppose you choose a marble at​ random, and do not replace it. Then you choose a second marble. Find the probability of the following event.

Question

Both of the selected marbles are red.

Answer 1

To find the probability that both selected marbles are red, you need to first find the total number of ways you can choose 2 marbles out of the 11 marbles in the jar, and then find the number of ways you can choose 2 red marbles out of the 4 red marbles.

Total number of ways to choose 2 marbles out of 11 marbles:
11 choose 2 = 11! / (2!(11-2)!) = 55

Number of ways to choose 2 red marbles out of 4 red marbles:
4 choose 2 = 4! / (2!(4-2)!) = 6

Therefore, the probability that both selected marbles are red is:
6 / 55 ≈ 0.1091 or 10.91%