To solve this problem, we will calculate the experimental probability of the spinner landing on the color green and then use this probability to predict the number of times the spinner will land on green in 50 spins. Here's the step-by-step solution:
1. Determine the total number of spins in the experiment:
The frequency for each color is given in the table, so we add these frequencies to find the total number of spins.
[tex]\[
\text{Total number of spins} = 7 (\text{Blue}) + 9 (\text{Red}) + 6 (\text{Green}) + 8 (\text{Yellow}) = 30
\][/tex]
2. Calculate the experimental probability of the spinner landing on green:
The probability of landing on green is the frequency of green outcomes divided by the total number of spins.
[tex]\[
\text{Probability of green} = \frac{\text{Frequency of green outcomes}}{\text{Total number of spins}} = \frac{6}{30} = \frac{1}{5} = 0.2
\][/tex]
3. Use the experimental probability to predict the number of green spins in 50 spins:
To find the predicted number of green spins when the spinner is spun 50 times, we multiply the probability of landing on green by the total number of spins.
[tex]\[
\text{Predicted number of green spins} = \text{Probability of green} \times \text{Number of spins} = 0.2 \times 50 = 10
\][/tex]
So, based on the given frequencies and the experimental probability, if the experiment is repeated with 50 spins, it is predicted that the spinner will land on green 10 times.
Therefore, the correct answer is:
[tex]\[
\boxed{10}
\][/tex]
