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A wheel has 10 equally sized slices numbered from 1 to 10.Some are grey and some are white.The slice numbered 3 is grey.The slices numbered 1, 2, 4, 5, 6, 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 PX be the probability of X.Let not X be the event that the wheel stops on a slice that is not white, and let Pnot 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.Event Outcomes Probability1 2 3 4 5 6 7 8 9 10X =PXnot X =PnotX(b)Subtract.=−1PnotX (c)Select the answer that makes the sentence true.

Question

A wheel has 10 equally sized slices numbered from 1 to 10.Some are grey and some are white.The slice numbered 3 is grey.The slices numbered 1, 2, 4, 5, 6, 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 PX be the probability of X.Let not X be the event that the wheel stops on a slice that is not white, and let Pnot 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.Event Outcomes Probability1 2 3 4 5 6 7 8 9 10X =PXnot X =PnotX(b)Subtract.=−1PnotX (c)Select the answer that makes the sentence true.

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Solution

(a) The event X includes the outcomes 1, 2, 4, 5, 6, 7, 8, 9, and 10. These are the white slices. The probability of X, PX, is 9/10 because there are 9 white slices out of a total of 10.

The event not X includes the outcome 3. This is the grey slice. The probability of not X, Pnot X, is 1/10 because there is 1 grey slice out of a total of 10.

Event Outcomes Probability X 1, 2, 4, 5, 6, 7, 8, 9, 10 = 9/10 not X 3 = 1/10

(b) Subtracting Pnot X from 1 gives 1 - 1/10 = 9/10. This is the same as PX, as expected because the probabilities of all possible outcomes must add up to 1.

(c) The sentence "The sum of the probabilities of all possible outcomes is 1" is true.

This problem has been solved

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