To find the probability that one jelly bean is red and the other jelly bean is green, we can use the following steps:
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Total Jelly Beans Calculation:
- Red jelly beans: 6
- Blue jelly beans: 4
- Green jelly beans: 6
- Total jelly beans = 6 + 4 + 6 = 16
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Total Ways to Choose 2 Jelly Beans: The total number of ways to choose 2 jelly beans from 16 can be calculated using the combination formula \(\binom{n}{r}\), which is defined as \(\frac{n!}{r!(n - r)!}\).
\[ \text{Total ways to choose 2 jelly beans} = \binom{16}{2} = \frac{16 \times 15}{2 \times 1} = 120 \]
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Ways to Choose 1 Red and 1 Green Jelly Bean:
- The number of ways to choose 1 red jelly bean from 6: \(\binom{6}{1} = 6\)
- The number of ways to choose 1 green jelly bean from 6: \(\binom{6}{1} = 6\)
Therefore, the number of ways to choose 1 red and 1 green jelly bean is: \[ \text{Ways to choose 1 red and 1 green} = 6 \times 6 = 36 \]
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Probability Calculation: The probability that one jelly bean is red and the other is green is given by the ratio of the number of favorable outcomes (choosing 1 red and 1 green) to the total outcomes (choosing any 2 jelly beans):
\[ P(\text{1 red and 1 green}) = \frac{\text{Ways to choose 1 red and 1 green}}{\text{Total ways to choose 2 jelly beans}} = \frac{36}{120} \]
Thus, the probability that one jelly bean is red and the other jelly bean is green is:
\[ \frac{36}{120} \]
You do not need to simplify it as per your request, so the final answer is:
\[ \frac{36}{120} \]