To find the probability of drawing a green marble followed by a yellow marble in Kathleen's experiment, we first need to determine the total number of draws.
The total number of times Kathleen drew marbles can be calculated by adding the number of times each color was drawn:
\[ 10 \text{ (Red)} + 4 \text{ (Blue)} + 8 \text{ (Green)} + 4 \text{ (Purple)} + 4 \text{ (Yellow)} = 30 \]
Now, we will find the individual probabilities for drawing a green marble and then drawing a yellow marble.
- Probability of drawing a green marble: The number of green marbles drawn is 8. Therefore, the probability \( P(\text{Green}) \) is:
\[ P(\text{Green}) = \frac{\text{Number of Green}}{\text{Total Draws}} = \frac{8}{30} = \frac{4}{15} \]
- Probability of drawing a yellow marble: The number of yellow marbles drawn is 4. Therefore, the probability \( P(\text{Yellow}) \) is:
\[ P(\text{Yellow}) = \frac{\text{Number of Yellow}}{\text{Total Draws}} = \frac{4}{30} = \frac{2}{15} \]
- Calculating the joint probability of drawing a green marble first and then a yellow marble: Since the draws are independent (due to the replacement of the marbles), the joint probability \( P(\text{Green, then Yellow}) \) is the product of the individual probabilities:
\[ P(\text{Green, then Yellow}) = P(\text{Green}) \times P(\text{Yellow}) = \frac{4}{15} \times \frac{2}{15} = \frac{8}{225} \]
Therefore, the probability that Kathleen would first draw a green marble and then draw a yellow marble is:
\[ \frac{8}{225} \]
You would need to choose the corresponding option from A, B, C, or D based on this calculated probability. If one of those matches \( \frac{8}{225} \), that would be the correct answer.
13 answers