We have a deck of 8 cards numbered from 1 to 8.Some are grey and some are white.The cards numbered 1 and 5 are grey.The cards numbered 2, 3, 4, 6, 7, and 8 are white.A card is drawn at random.Let X be the event that the drawn card is grey, and let PX be the probability of X.Let not X be the event that the drawn card is not grey, 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 8X =PXnot X =PnotX(b)Subtract.=−1PnotX (c)Select the answer that makes the sentence true.−1Pnot X is the same as ▼−1PX.
Question
We have a deck of 8 cards numbered from 1 to 8.Some are grey and some are white.The cards numbered 1 and 5 are grey.The cards numbered 2, 3, 4, 6, 7, and 8 are white.A card is drawn at random.Let X be the event that the drawn card is grey, and let PX be the probability of X.Let not X be the event that the drawn card is not grey, 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 8X =PXnot X =PnotX(b)Subtract.=−1PnotX (c)Select the answer that makes the sentence true.−1Pnot X is the same as ▼−1PX.
Solution 1
(a) The event X contains the outcomes 1 and 5, since these are the grey cards. The event not X contains the outcomes 2, 3, 4, 6, 7, and 8, since these are the white cards. The total number of outcomes is 8, so the probability of each event is the number of outcomes in the event divided by the total number of outcomes.
Event Outcomes Probability X 1, 5 PX = 2/8 = 0.25 not X 2, 3, 4, 6, 7, 8 Pnot X = 6/8 = 0.75
(b) Subtracting Pnot X from 1 gives 1 - 0.75 = 0.25.
(c) -1 * Pnot X is not the same as -1 * PX. The negative of a probability does not have a meaningful interpretation in this context. However, 1 - Pnot X is the same as PX, because the events X and not X are complementary (one of them must occur, and they cannot both occur).
Solution 2
(a) The event X includes the outcomes where the drawn card is grey. In this case, the grey cards are 1
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