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The image shows two spinners, each divided into four equal sections with different colors: Red (R), Blue (B), and Yellow (Y). The question asks for the probability that both spinners show the same color when spun once.

Here are the colors on the two spinners:
- Spinner 1: Red (R), Blue (B), Red (R), Yellow (Y)
- Spinner 2: Red (R), Blue (B), Yellow (Y), Blue (B)

### Steps to solve:
1. **Identify matching color pairs:**
   - The possible outcomes for the first spinner are \( R_1, B_1, R_1, Y_1 \) (2 Red, 1 Blue, 1 Yellow).
   - The possible outcomes for the second spinner are \( R_2, B_2, Y_2, B_2 \) (1 Red, 2 Blue, 1 Yellow).

2. **Match each color:**
   - Red (R) can match between the two spinners.
   - Blue (B) can match between the two spinners.
   - Yellow (Y) can match between the two spinners.

### Probability:
- Total possible outcomes for each spinner are \( 4 \times 4 = 16 \) outcomes (since each spinner has 4 sectors).
- Probability of matching:
  - Red (R) from Spinner 1 with Red (R) from Spinner 2: \(\frac{2}{4} \times \frac{1}{4} = \frac{2}{16}\).
  - Blue (B) from Spinner 1 with Blue (B) from Spinner 2: \(\frac{1}{4} \times \frac{2}{4} = \frac{2}{16}\).
  - Yellow (Y) from Spinner 1 with Yellow (Y) from Spinner 2: \(\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}\).

3. **Total Probability:**
   \[
   P(\text{same color}) = \frac{2}{16} + \frac{2}{16} + \frac{1}{16} = \frac{5}{16}.
   \]

Thus, the probability that both spinners show the same color is \( \frac{5}{16} \), or approximately 0.3125.

Would you like more details or have any questions?

### Relative questions:
1. What is the probability of getting a Red and Blue combination?
2. How would the probability change if one of the spinners had 3 colors instead of 4?
3. What if the spinners had 8 equal sections, how would that affect the calculations?
4. Can this problem be solved using conditional probability?
5. How does the inclusion of Yellow in both spinners affect the overall probability?

**Tip:** When working with spinners, always consider each color’s frequency to simplify probability calculations.

If each spinner is spun once, what is the probability that both spinners show the same color?

Solve the probability problem of two spinners showing the same color when spun once. Learn how to calculate matching probabilities using the multiplication rule and basic probability theorems. Suitable for students in Grades 7-10.

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