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.