https://r2.erweima.ai/mathbot/image/1726153186721lylhbhvw.jpg

To solve this problem, we need to calculate the **expected value** of the spinner.

### Steps:
1. **Identify possible outcomes**: The spinner has six sections, with the following values:
   - 1 appears 2 times
   - 2 appears 2 times
   - 3 appears 2 times

2. **Calculate the probabilities of each outcome**:
   Since the spinner is divided into six equal sections, the probability of landing on any given section is \( \frac{1}{6} \).

3. **List the possible outcomes and their probabilities**:
   - Probability of landing on 1: \( \frac{2}{6} = \frac{1}{3} \)
   - Probability of landing on 2: \( \frac{2}{6} = \frac{1}{3} \)
   - Probability of landing on 3: \( \frac{2}{6} = \frac{1}{3} \)

4. **Calculate the expected value**:
   The formula for expected value is:

   \[
   E(X) = \sum ( \text{value} \times \text{probability} )
   \]
   
   So, the expected value is:

   \[
   E(X) = (1 \times \frac{1}{3}) + (2 \times \frac{1}{3}) + (3 \times \frac{1}{3})
   \]

   \[
   E(X) = \frac{1}{3} + \frac{2}{3} + \frac{3}{3}
   \]

   \[
   E(X) = \frac{6}{3} = 2
   \]

### Conclusion:
The expected value of the spinner is **2**.

The correct answer is **(b) 2**.

Would you like further details or clarification on any part of this solution?

### Related Questions:
1. What is the probability of landing on a 3?
2. How do you calculate expected value with unequal probabilities?
3. What is the variance of the values on this spinner?
4. How would the expected value change if there were more sections with different values?
5. How is the concept of expected value applied in real-life situations?

### Tip:
When dealing with equally likely outcomes, calculating the expected value is a straightforward process that only involves summing up the products of outcomes and their probabilities.

What is the expected value of the spinner shown?

Calculate the expected value of a spinner with sections labeled 1, 2, and 3. Learn how to use probabilities and expected value formulas to solve this problem, suitable for middle school students in Grades 6-8.

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