Question

A jar contains 5 red and 5 yellow Starburst candies. You draw two Starbursts without replacement. What is the probability that both Starbursts are red?(1 point)
Responses

29
2 ninths

110
1 tenth

245
2 over 45

15

Answer 1

To find the probability that both Starbursts drawn from the jar are red, we can follow these steps:

1. **Total number of candies**: There are 5 red and 5 yellow Starburst candies, so the total number of candies is \( 5 + 5 = 10 \).

2. **Calculating the probability of the first draw**:
- The probability of drawing a red Starburst first is:
\[
P(\text{first red}) = \frac{5}{10} = \frac{1}{2}
\]

3. **Calculating the probability of the second draw** (given that the first one drawn was red):
- After drawing one red Starburst, there are now 4 red candies and 5 yellow candies left, making the total number of candies now 9.
- The probability of drawing a red Starburst second is:
\[
P(\text{second red | first red}) = \frac{4}{9}
\]

4. **Calculating the combined probability**:
- The combined probability of both events happening (drawing a red first and then a red second) is:
\[
P(\text{both red}) = P(\text{first red}) \times P(\text{second red | first red}) = \frac{1}{2} \times \frac{4}{9} = \frac{4}{18} = \frac{2}{9}
\]

Therefore, the probability that both Starbursts drawn are red is \(\frac{2}{9}\).

Thus, the correct response is: **2 ninths**.