Eight balls numbered from 1 to 8 are placed into a bag.Some are grey and some are white.The balls numbered 2, 3, 4, 5, and 7 are grey.The balls numbered 1, 6, and 8 are white.A ball is selected at random.Let X be the event that the selected ball is white, and let PX be the probability of X.Let not X be the event that the selected ball 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 8X =PXnot X =PnotX(b)Subtract.=−1PX (c)Select the answer that makes the sentence true.−1PX is the same as ▼(Choose one).CheckSave For LaterSubmit Assignment
Question
Eight balls numbered from 1 to 8 are placed into a bag.Some are grey and some are white.The balls numbered 2, 3, 4, 5, and 7 are grey.The balls numbered 1, 6, and 8 are white.A ball is selected at random.Let X be the event that the selected ball is white, and let PX be the probability of X.Let not X be the event that the selected ball 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 8X =PXnot X =PnotX(b)Subtract.=−1PX (c)Select the answer that makes the sentence true.−1PX is the same as ▼(Choose one).CheckSave For LaterSubmit Assignment
Solution
(a) For the event X (the ball selected is white), the outcomes are 1, 6, and 8. Since there are 8 balls in total, the probability PX is 3/8.
Event: X Outcomes: 1, 6, 8 Probability: PX = 3/8
For the event not X (the ball selected is not white, i.e., grey), the outcomes are 2, 3, 4, 5, and 7. The probability Pnot X is 5/8.
Event: not X Outcomes: 2, 3, 4, 5, 7 Probability: Pnot X = 5/8
(b) Subtracting PX from 1 gives 1 - PX = 1 - 3/8 = 5/8, which is the same as Pnot X.
(c) Therefore, 1 - PX is the same as Pnot X.
Similar Questions
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