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a wheel has 8 equally sized slices numbered from 1 to 8.
some are grey and some are white.
the slices numbered 1, 2, 3, 5, 6, and 8 are grey.
the slices numbered 4 and 7 are white.
the wheel is spun and stops on a slice at random.
let x be the event that the wheel stops on a white slice, and let p(x) be the
probability of x.
let not x be the event that the wheel stops on a slice that is not white, and let
p(not x) be the probability of not x.
(a) for each event in the table, check the outcome(s) that are contained in the event. then, in the last column, enter the probability of the event.

Explanation:

Step1: Determine the total number of slices

The wheel has 8 equally - sized slices, so the total number of possible outcomes \(n = 8\).

Step2: Find the number of favorable outcomes for event \(X\)

Event \(X\) is the wheel stopping on a white slice. The white - numbered slices are 4 and 7. So the number of favorable outcomes for \(X\), \(m_X=2\).
Using the probability formula \(P(X)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), we have \(P(X)=\frac{2}{8}=\frac{1}{4}\).

Step3: Find the number of favorable outcomes for event \(not - X\)

Event \(not - X\) is the wheel stopping on a non - white slice. The non - white (grey) numbered slices are 1, 2, 3, 5, 6, 8. So the number of favorable outcomes for \(not - X\), \(m_{not - X}=6\).
Using the probability formula \(P(not - X)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), we have \(P(not - X)=\frac{6}{8}=\frac{3}{4}\).

Answer:

For event \(X\):

• Outcomes: Check the boxes for 4 and 7.
• Probability: \(P(X)=\frac{1}{4}\)

For event \(not - X\):

• Outcomes: Check the boxes for 1, 2, 3, 5, 6, 8.
• Probability: \(P(not - X)=\frac{3}{4}\)