Let's analyze the problem step-by-step:

1. Identifying the White and Grey Slices:

   • From the image, there are 6 numbered slices.
   • White slices: 1, 2, and 6.
   • Grey slices: 3, 4, and 5.

2. Total Number of Slices:

   • There are a total of 6 equally sized slices.

Now, let’s address each question:

Part (a)

The question asks for the probability that the wheel stops on a white slice.

• Total possible outcomes (all slices): 6
• Favorable outcomes (white slices): 3 (slices 1, 2, and 6)

The probability $P(\text{white})$ is: $P(\text{white}) = \frac{\text{Number of white slices}}{\text{Total slices}} = \frac{3}{6} = \frac{1}{2}$

Part (b)

The question asks for the probability that the wheel stops on a white slice, given that it stops on a number less than 5.

• Condition: The slice number is less than 5, so we only consider slices 1, 2, 3, and 4.
• White slices under this condition: 1 and 2.
• Total slices under this condition: 4 (slices 1, 2, 3, and 4).

The conditional probability $P(\text{white} \mid \text{number} < 5)$ is: $P(\text{white} \mid \text{number} < 5) = \frac{\text{Number of white slices less than 5}}{\text{Total slices less than 5}} = \frac{2}{4} = \frac{1}{2}$

Final Answers

• (a) $\frac{1}{2}$
• (b) $\frac{1}{2}$

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

Related Questions for Further Practice:

1. What is the probability that the wheel stops on a grey slice?
2. If the wheel is spun twice, what is the probability it stops on white both times?
3. What is the probability that the wheel stops on an odd-numbered white slice?
4. If the wheel stops on an even number, what is the probability it is a grey slice?
5. What is the probability that the wheel stops on a number greater than 3?

Tip: When dealing with probability, always identify the total number of outcomes and the number of favorable outcomes to set up your fraction accurately.