Let's solve the problems given in the image step-by-step.

Part (a)

Question: What is the probability that the wheel stops on a white slice?

1. Count the total slices: The spinner has 10 equally sized slices numbered 1 to 10.

2. Identify white slices: Based on the image, the white slices are: 1, 3, 5, 7, and 9, totaling 5 white slices.

3. Calculate the probability: Since each slice has an equal probability of being landed on, the probability of stopping on a white slice is the ratio of white slices to total slices.

   $P(\text{white slice}) = \frac{\text{number of white slices}}{\text{total slices}} = \frac{5}{10} = \frac{1}{2}$

So, the answer to (a) is: $\frac{1}{2}$

Part (b)

Question: What is the probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9?

1. Identify the relevant numbers: The numbers less than 9 on the spinner are 1, 2, 3, 4, 5, 6, 7, and 8, making a total of 8 possible outcomes.

2. Identify the white slices among these: The white slices among the numbers less than 9 are 1, 3, 5, and 7, totaling 4 white slices.

3. Calculate the conditional probability: Given that the wheel stops on a number less than 9, we are interested in the probability it stops on a white slice. This probability is the ratio of white slices less than 9 to the total numbers less than 9.

   $P(\text{white slice} \mid \text{number} < 9) = \frac{\text{number of white slices less than 9}}{\text{total numbers less than 9}} = \frac{4}{8} = \frac{1}{2}$

So, the answer to (b) is: $\frac{1}{2}$

Would you like more details on any of these steps, or have any questions?

Here are some related questions to consider:

1. If there were 12 slices with the same color pattern, how would the probabilities change?
2. What if the spinner was spun twice? What would be the probability of landing on a white slice both times?
3. How would the probability change if we wanted the wheel to land on an odd-numbered slice?
4. What is the probability that the spinner lands on a number greater than 5 and a white slice?
5. If the slices were numbered differently, say with odd numbers only, how would this affect the calculation?

Tip: Remember that conditional probability is the probability of an event occurring given that another event has already occurred. It often reduces the total number of possible outcomes.