To find the probability of selecting one red jelly bean and one green jelly bean from the jar, we can follow these steps:
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Count the total number of jelly beans in the jar:
- Red jelly beans: 6
- Blue jelly beans: 4
- Green jelly beans: 6
- Total = 6 + 4 + 6 = 16 jelly beans
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Calculate the number of ways to select one red jelly bean and one green jelly bean:
- The number of ways to choose 1 red jelly bean from 6 is \( \binom{6}{1} = 6 \).
- The number of ways to choose 1 green jelly bean from 6 is \( \binom{6}{1} = 6 \).
- Therefore, the total number of ways to choose one red and one green jelly bean is: \[ 6 \times 6 = 36 \text{ ways} \]
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Calculate the total number of ways to choose 2 jelly beans from the 16 available:
- The number of ways to choose 2 jelly beans from 16 is \( \binom{16}{2} \).
- Calculating \( \binom{16}{2} \): \[ \binom{16}{2} = \frac{16 \times 15}{2 \times 1} = 120 \]
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Calculate the probability:
- The probability of choosing one red and one green jelly bean is the ratio of the number of favorable outcomes to the total outcomes: \[ P(\text{1 red and 1 green}) = \frac{36}{120} \]
Thus, the probability that one jelly bean is red and the other is green is:
\[ \frac{36}{120} \]
This result is in fraction form as requested, and it can be simplified if needed, but you don't need to simplify for your answer.