To find the probability of selecting one red jelly bean and one green jelly bean from the jar, we need to calculate the total number of ways to choose two jelly beans and the number of favorable outcomes for our event (one red and one green).
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Total number of jelly beans: \[ 6 \text{ (red)} + 4 \text{ (blue)} + 6 \text{ (green)} = 16 \text{ jelly beans} \]
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Total ways to choose 2 jelly beans out of 16: The number of ways to choose 2 jelly beans from 16 is given by the combination formula \( \binom{n}{k} \), which calculates the number of ways to choose \( k \) items from \( n \) items: \[ \binom{16}{2} = \frac{16 \times 15}{2 \times 1} = 120 \]
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Ways to choose 1 red and 1 green jelly bean:
- The number of ways to choose 1 red from 6 is: \[ \binom{6}{1} = 6 \]
- The number of ways to choose 1 green from 6 is: \[ \binom{6}{1} = 6 \]
- Therefore, the number of ways to choose 1 red and 1 green jelly bean is: \[ 6 \times 6 = 36 \]
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Probability of choosing one red and one green jelly bean: The probability is given by the ratio of the number of favorable outcomes (choosing one red and one green) to the total outcomes (choosing any two jelly beans): \[ P(\text{1 red, 1 green}) = \frac{36}{120} \]
Thus, the probability that one jelly bean is red and the other is green is: \[ \frac{36}{120} \]
This fraction is the final answer, as you indicated not to simplify it further.