A wheel has 5 equally sized slices numbered from 1 to 5.Some are grey and some are white.The slices numbered 2 and 3 are grey.The slices numbered 1, 4, and 5 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 5X =PXnot X =PnotX(b)Subtract.=−1PnotX (c)Select the answer that makes the sentence true.−1Pnot X is the same as ▼(Choose one).
Question
A wheel has 5 equally sized slices numbered from 1 to 5.Some are grey and some are white.The slices numbered 2 and 3 are grey.The slices numbered 1, 4, and 5 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 5X =PXnot X =PnotX(b)Subtract.=−1PnotX (c)Select the answer that makes the sentence true.−1Pnot X is the same as ▼(Choose one).
Solution
(a) The event X includes outcomes 1, 4, and 5, which are the white slices. Since there are 5 slices in total and 3 of them are white, the probability of X, PX, is 3/5 or 0.6.
The event not X includes outcomes 2 and 3, which are the grey slices. Since there are 5 slices in total and 2 of them are grey, the probability of not X, Pnot X, is 2/5 or 0.4.
Event Outcomes Probability 1 2 3 4 5 X ✔ ✔ ✔ = 3/5 not X ✔ ✔ = 2/5
(b) Subtracting Pnot X from 1 gives 1 - 2/5 = 3/5, which is the same as PX.
(c) 1 - Pnot X is the same as PX.
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