Question

Suppose a jar contains 13 red marbles and 40 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red. Round to 3 decimal places.

Answer 1

37 + 11 = 48 marbles in total.

At our first pull, there is an 11/48 chance that a red will be pulled--the number of red out of the total number.

At the second pull there is a 10/47 chance that the second marble will be red as well--how many red/total are still in there.

From here, we multiply our two fractions together:

11/48 * 10/47

We can do a little bit of simplifying first; 10 and 48 both have a 2 in common:

11/24 * 5/47

Now we multiply our numerators (11 *5) and denominators (24 * 47) and our answer is:

55/1128, or 55:1128

When we divide, we get about 0.04876, which rounds to 4.88%, depending if you want to keep it in fraction, ratio, or percentage form.