Questions: A wheel has 10 equally sized slices numbered from 1 to 10. Some are grey and some are white. The slices numbered 1, 2, and 6 are grey. The slices numbered 3,4,5,7,8,9, and 10 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. 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.

A wheel has 10 equally sized slices numbered from 1 to 10. Some are grey and some are white. The slices numbered 1, 2, and 6 are grey. The slices numbered 3,4,5,7,8,9, and 10 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. 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.

Transcript text: A wheel has 10 equally sized slices numbered from 1 to 10. Some are grey and some are white. The slices numbered 1, 2, and 6 are grey. The slices numbered 3,4,5,7,8,9, and 10 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. 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.

Solution

Solution Steps

Step 1: Identify the white and non-white slices

The wheel has 10 slices numbered from 1 to 10.
White slices: 3, 4, 5, 7, 8, 9, 10.
Non-white slices: 1, 2, 6.

Step 2: Determine the probability of event \(X\)

Event \(X\): The wheel stops on a white slice.
Number of white slices: 7.
Total number of slices: 10.
Probability of \(X\), \(P(X)\) = Number of white slices / Total number of slices = 7/10.

Step 3: Determine the probability of event \( \text{not } X \)

Event \( \text{not } X \): The wheel stops on a non-white slice.
Number of non-white slices: 3.
Total number of slices: 10.
Probability of \( \text{not } X \), \(P(\text{not } X)\) = Number of non-white slices / Total number of slices = 3/10.