https://file.aiquickdraw.com/mathbot/file/17285510013737h1i01d6.jpg

Let's analyze the image step by step to answer the questions.

### Spinner Breakdown:
- The spinner has 8 equally sized slices numbered 1 to 8.
- Some slices are white, and some are grey.

From the image:
- **Grey slices**: 2, 3, 6, and 7.
- **White slices**: 1, 4, 5, and 8.

Now let's solve the two parts:

### Part (a) Probability that the wheel stops on a grey slice:
- There are 4 grey slices out of a total of 8 slices.
- The probability of landing on a grey slice is:
  \[
  \frac{\text{Number of grey slices}}{\text{Total slices}} = \frac{4}{8} = \frac{1}{2}.
  \]
  So, the probability is **1/2**.

### Part (b) Probability that the wheel stops on a grey slice, given that it stops on an even-numbered slice:
- First, identify the even-numbered slices: 2, 4, 6, and 8.
- Out of these even-numbered slices, the grey ones are 2 and 6. So, 2 out of 4 even-numbered slices are grey.
- The conditional probability is:
  \[
  \frac{\text{Number of grey even-numbered slices}}{\text{Total even-numbered slices}} = \frac{2}{4} = \frac{1}{2}.
  \]
  So, the probability is **1/2**.

### Summary:
- (a) Probability of landing on a grey slice: \( \frac{1}{2} \).
- (b) Probability of landing on a grey slice given it's an even-numbered slice: \( \frac{1}{2} \).

Would you like more details on conditional probability or the reasoning behind these steps? Feel free to ask any questions.

Here are 5 related questions for practice:
1. What is the probability that the wheel stops on a white slice?
2. What is the probability that the wheel stops on an odd-numbered slice?
3. If the spinner is spun twice, what is the probability of landing on a grey slice both times?
4. What is the probability that the wheel stops on a slice numbered greater than 4?
5. What is the probability of landing on a white slice, given that the number is odd?

**Tip:** Conditional probability helps refine chances based on additional information. When you have "given" conditions, reduce the sample space to only the relevant cases.

A spinner has 8 equally sized slices numbered from 1 to 8. Some are white and some are grey. (a) What is the probability that the wheel stops on a grey slice? (b) What is the probability that the wheel stops on a grey slice, given that it stops on an even-numbered slice?

Learn how to calculate the probability of a spinner landing on a grey slice. This problem covers basic probability and conditional probability, using real-life examples such as a spinner with numbered slices. Suitable for students in Grades 6-8.

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