https://file.aiquickdraw.com/mathbot/file/1726805944978l24w16ro.jpg

The image presents a spinner divided into four colors: **Purple**, **Pink**, **Blue**, and **Yellow**, with frequencies provided for each color:

- Purple: 12
- Pink: 6
- Yellow: 9
- Blue: 13

The question asks: **If Jim spins the spinner 16 times, how many times would you predict the spinner to land on blue based on theoretical probability?**

### Step 1: Calculate the total frequency
We add up the frequencies for all the colors:
\[
12 + 6 + 9 + 13 = 40
\]
So, the total number of outcomes for the spinner is 40.

### Step 2: Calculate the probability of landing on blue
The probability of landing on blue is the frequency of blue divided by the total frequency:
\[
P(\text{Blue}) = \frac{13}{40}
\]

### Step 3: Predict the number of times blue will appear in 16 spins
To find how many times the spinner is expected to land on blue in 16 spins, we multiply the probability by the number of spins:
\[
\text{Expected spins on blue} = P(\text{Blue}) \times 16 = \frac{13}{40} \times 16 = \frac{208}{40} = 5.2
\]

### Conclusion:
Jim can expect the spinner to land on blue approximately **5 times** out of 16 spins.

Would you like a further breakdown of this explanation, or do you have any other questions?

### Related Questions:
1. What is the probability of landing on purple?
2. If Jim spins the spinner 100 times, how many times would it land on yellow?
3. How would the results differ if the spinner was spun 20 times instead of 16?
4. How do experimental probabilities compare with theoretical probabilities in such experiments?
5. How can you represent the results of these probabilities graphically?

### Tip:
When working with probabilities, always confirm that the sum of individual probabilities equals 1 to verify accuracy!

If Jim spins the spinner 16 times, how many times would you predict the spinner to land on blue based on theoretical probability?

Calculate how many times a spinner will land on blue in 16 spins using theoretical probability. The problem involves frequency analysis and probability calculation with step-by-step guidance. Suitable for Grades 6-8 students.

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