A jar contains jelly beans. There are
6 red jelly beans,
6 blue jelly beans and
5 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.
There are a total of 17 jelly beans in the jar.
To calculate the probability, we need to consider the different possibilities of selecting one red jelly bean and one green jelly bean.
First, we can select a red jelly bean and then a green jelly bean:
Probability of selecting a red jelly bean = 6/17
Probability of selecting a green jelly bean (after selecting a red jelly bean) = 5/16
The total probability of this sequence is (6/17) * (5/16) = 30/272
Second, we can select a green jelly bean and then a red jelly bean:
Probability of selecting a green jelly bean = 5/17
Probability of selecting a red jelly bean (after selecting a green jelly bean) = 6/16
The total probability of this sequence is (5/17) * (6/16) = 30/272
Adding up these two probabilities gives us the overall probability of selecting one red jelly bean and one green jelly bean:
(30/272) + (30/272) = 60/272
Therefore, the probability that one jelly bean is red and the other jelly bean is green is 60/272.