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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.Which statement about probability is true?

The probability of landing on blue is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on orange.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.

To analyze the probabilities of landing on different colors, let's first count the sections for each color:

- **Purple:** 2 sections (1, 8)
- **Yellow:** 2 sections (2, 3)
- **Blue:** 3 sections (4, 5, 6)
- **Orange:** 1 section (7)

Now, let's calculate the probabilities for each color. Since there are 8 sections total, each section has a probability of \( \frac{1}{8} \).

- **Probability of landing on purple:** \( \frac{2}{8} = \frac{1}{4} = 0.25 \)
- **Probability of landing on yellow:** \( \frac{2}{8} = \frac{1}{4} = 0.25 \)
- **Probability of landing on blue:** \( \frac{3}{8} = 0.375 \)
- **Probability of landing on orange:** \( \frac{1}{8} = 0.125 \)

Next, we analyze each statement given the probabilities calculated:

1. **The probability of landing on blue is greater than the probability of landing on purple.**
   - True, \( 0.375 > 0.25 \).

2. **The probability of landing on yellow is less than the probability of landing on orange.**
   - False, \( 0.25 > 0.125 \).

3. **The probability of landing on orange is equal to the probability of landing on yellow.**
   - False, \( 0.125 \neq 0.25 \).

4. **The probability of landing on purple is equal to the probability of landing on blue.**
   - False, \( 0.25 \neq 0.375 \).

So, the correct statement is: **The probability of landing on blue is greater than the probability of landing on purple.**

Would you like further details or have any questions?

Here are 8 related questions to expand on this topic:
1. How would the probabilities change if there were 10 sections in total?
2. What is the probability of landing on either purple or yellow?
3. If the spinner is spun twice, what is the probability of landing on blue both times?
4. How would you calculate the expected number of spins to land on orange?
5. If you add one more purple section, what is the new probability of landing on purple?
6. What is the probability of not landing on blue?
7. How does the concept of mutually exclusive events apply to this spinner?
8. Can you create a formula to generalize the probability of landing on any color based on the number of sections?

**Tip:** When calculating probabilities, always ensure that the total probability sums to 1. This can help verify the correctness of your calculations.

Explore the concept of probability using a spinner with sections colored purple, yellow, blue, and orange. Learn how to calculate probabilities for different colors and analyze statements about probabilities. Suitable for Grades 7-9.

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