Question

A jar contains jelly beans. There are
6 red jelly beans,
4 blue jelly beans and
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. Click Here for Help Video

Answer 1

To find the probability of selecting one red jelly bean and one green jelly bean from the jar, we can follow these steps:

1. **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

2. **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:
\[
6 \times 6 = 36 \text{ ways}
\]

3. **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 \( \binom{16}{2} \):
\[
\binom{16}{2} = \frac{16 \times 15}{2 \times 1} = 120
\]

4. **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.