A jar contains jelly beans. There are
4
4 red jelly beans,
4
4 blue jelly beans and
6
6 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 4 + 4 + 6 = 14.
To find the probability of drawing one red jelly bean and one green jelly bean, we need to consider two cases:
Case 1: Drawing a red jelly bean first and then a green jelly bean.
In this case, the probability of drawing a red jelly bean is 4/14, and after removing one red jelly bean, we are left with 13 jelly beans in total. The probability of drawing a green jelly bean from the remaining 13 jelly beans is 6/13. Therefore, the probability of this case is (4/14) * (6/13).
Case 2: Drawing a green jelly bean first and then a red jelly bean.
In this case, the probability of drawing a green jelly bean is 6/14, and after removing one green jelly bean, we are left with 13 jelly beans in total. The probability of drawing a red jelly bean from the remaining 13 jelly beans is 4/13. Therefore, the probability of this case is (6/14) * (4/13).
To find the probability of either Case 1 or Case 2 happening, we need to add the probabilities of both cases together:
(4/14) * (6/13) + (6/14) * (4/13) = 24/182 + 24/182 = 48/182 = 24/91
Therefore, the probability of drawing one jelly bean being red and the other jelly bean being green is 24/91.