a. The probability that the wheel stops on a grey slice is 3/5.
b. The probability that the wheel stops on a grey slice, given that the wheel stops on a number less than 9, is 3/4.
How to calculate the probability of the wheel
(a) To calculate the probability of the wheel stopping on a grey slice, determine the ratio of the number of grey slices to the total number of slices.
Number of grey slices: 6
Total number of slices: 10
Probability of stopping on a grey slice = Number of grey slices / Total number of slices
Probability of stopping on a grey slice = 6/10 = 3/5
Therefore, the probability that the wheel stops on a grey slice is 3/5.
b. To find the probability that the wheel stops on a grey slice, given that the wheel stops on a number less than 9, consider the favorable outcomes (grey slices with numbers less than 9) and divide it by the total outcomes (slices with numbers less than 9):
Number of favorable outcomes = Number of grey slices with numbers less than 9 = 6 (slices 1, 2, 3, 5, 7, 8)
Total number of outcomes = Number of slices with numbers less than 9 = 8 (slices 1, 2, 3, 4, 5, 6, 7, 8)
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 6 / 8
Simplifying the fraction
Probability = 3 / 4
Therefore, the probability that the wheel stops on a grey slice, given that the wheel stops on a number less than 9, is 3/4.