Question

Mrs. Booker's class is conducting an experiment to find the probability of pulling certain colors from a bag of 25 marbles. If 4 are purple, 6 are yellow, 4 are green, and the rest are black, what is the probability of drawing 2 purple if the marbles are not replaced after they are picked? Show answer as a percent rounded to nearest hundredth, if necessary.
A.
1.92%
B.
2.56%
C.
2.67%
D.
2%

Answer 1

To find the probability of drawing 2 purple marbles from a bag of 25 marbles, we need to use the formula for probability without replacement.

1. **Determine the total number of marbles and the number of purple marbles:**
- Total marbles = 25
- Purple marbles = 4

2. **Calculate the probability of drawing the first purple marble:**
\[
P(\text{1st purple}) = \frac{4}{25}
\]

3. **Calculate the probability of drawing the second purple marble after the first one has been drawn (without replacement):**
- Once the first purple marble is drawn, there are now 3 purple marbles left and a total of 24 marbles remaining.
\[
P(\text{2nd purple | 1st purple}) = \frac{3}{24} = \frac{1}{8}
\]

4. **Now, calculate the combined probability of both events happening (drawing 2 purple marbles):**
\[
P(\text{2 purple}) = P(\text{1st purple}) \times P(\text{2nd purple | 1st purple}) = \frac{4}{25} \times \frac{3}{24}
\]
\[
P(\text{2 purple}) = \frac{4 \times 3}{25 \times 24} = \frac{12}{600} = \frac{1}{50}
\]

5. **Convert the fraction to a percentage:**
\[
P(\text{2 purple}) = \frac{1}{50} = 0.02 \text{ as a decimal}
\]
To convert to a percentage, multiply by 100:
\[
0.02 \times 100 = 2\%
\]

Thus, the probability of drawing 2 purple marbles is **2%**.

The correct answer is **D. 2%**.