A jar contains jelly beans. There are

Question

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:

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