A jar contains jelly beans. There are
six yellow jelly beans,
six blue jelly beans and
five green jelly beans. You randomly take two jelly beans out to eat. Are you more likely to draw two straight yellow jelly beans or a blue and green?
To determine which outcome is more likely, we need to find the probabilities of drawing two straight yellow jelly beans and the probability of drawing a blue and green jelly bean.
The total number of jelly beans in the jar is 6 yellow + 6 blue + 5 green = 17.
The probability of drawing two straight yellow jelly beans can be calculated using the formula for probability:
P(two straight yellow) = (number of ways to draw two yellow jelly beans) / (total number of possible outcomes)
The number of ways to draw two yellow jelly beans is given by combinations, which can be calculated as:
C(6, 2) = 6! / (2! * (6-2)!) = 15
Since we are taking two jelly beans out, the total number of possible outcomes is calculated as combinations of 17 objects taken 2 at a time:
C(17, 2) = 17! / (2! * (17-2)!) = 136
Therefore, the probability of drawing two straight yellow jelly beans is:
P(two straight yellow) = 15 / 136 ≈ 0.110
Similarly, the probability of drawing a blue and green jelly bean can be calculated as:
P(blue and green) = (number of ways to draw one blue and one green jelly bean) / (total number of possible outcomes)
The number of ways to draw one blue and one green jelly bean is:
(number of blue jelly beans) * (number of green jelly beans) = 6 * 5 = 30
So the probability of drawing a blue and green jelly bean is:
P(blue and green) = 30 / 136 ≈ 0.221
Comparing the two probabilities, we find that P(blue and green) ≈ 0.221 > P(two straight yellow) ≈ 0.110. Therefore, it is more likely to draw a blue and green jelly bean rather than two straight yellow jelly beans.