Question

A jar contains jelly beans. There are
9 red jelly beans,
10 blue jelly beans and
7 green jelly beans. You randomly take two jelly beans out to eat. What is the probability that both are blue? Write your answer as a fraction. You do not need to simplif

Answer 1

To calculate the probability that both jelly beans drawn are blue, we need to first determine the total number of jelly beans and then find the number of ways to choose 2 blue jelly beans from the total.

1. **Total number of jelly beans:**
- Red: 9
- Blue: 10
- Green: 7
- Total = 9 + 10 + 7 = 26 jelly beans

2. **Number of ways to choose 2 jelly beans from the total:**
We can calculate this using the combination formula \(\binom{n}{r}\), which represents the number of ways to choose \(r\) objects from \(n\).
\[
\text{Total ways to choose 2 jelly beans} = \binom{26}{2} = \frac{26 \times 25}{2 \times 1} = 325
\]

3. **Number of ways to choose 2 blue jelly beans:**
Using the same combination formula, we find:
\[
\text{Ways to choose 2 blue jelly beans} = \binom{10}{2} = \frac{10 \times 9}{2 \times 1} = 45
\]

4. **Probability that both jelly beans drawn are blue:**
The probability \(P\) is given by the formula:
\[
P(\text{both blue}) = \frac{\text{Number of ways to choose 2 blue}}{\text{Total ways to choose 2}} = \frac{45}{325}
\]

Thus, the probability that both jelly beans drawn are blue is:

\[
\frac{45}{325}
\]