A jar contains jelly beans. There are
six red jelly beans,
six blue jelly beans and
five green jelly beans. You randomly take two jelly beans out to eat. What is the probability that one jelly bean is red and the other jelly bean is green? Write your answer as a fraction. You do not need to simplify.
The total number of jelly beans in the jar is 6 + 6 + 5 = 17.
To calculate the probability, we need to find the number of favorable outcomes, i.e., the number of ways to choose one red jelly bean and one green jelly bean.
Since there are 6 red jelly beans and 5 green jelly beans, the number of ways to choose one red and one green is 6 * 5 = 30.
Now, we need to find the total number of possible outcomes, i.e., the number of ways to choose any two jelly beans from the 17 total jelly beans.
The number of ways to choose 2 jelly beans out of 17 is C(17, 2) = (17!)/(2! * (17-2)!) = 17 * 16 / 2 = 136.
Therefore, the probability is 30/136 which can be simplified to 15/68.