A dartboard has 8 equally sized slices numbered from 1 to 8.Some are grey and some are white.The slices numbered 3, 4, 5, 6, 7, and 8 are grey.The slices numbered 1 and 2 are white.A dart is tossed and lands on a slice at random.Let X be the event that the dart lands on a grey slice, and let PX be the probability of X.Let not X be the event that the dart lands on a slice that 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.=−1PX (c)Select the answer that makes the sentence true.−1PX is the same as ▼(Choose one).
Question
A dartboard has 8 equally sized slices numbered from 1 to 8.Some are grey and some are white.The slices numbered 3, 4, 5, 6, 7, and 8 are grey.The slices numbered 1 and 2 are white.A dart is tossed and lands on a slice at random.Let X be the event that the dart lands on a grey slice, and let PX be the probability of X.Let not X be the event that the dart lands on a slice that 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.=−1PX (c)Select the answer that makes the sentence true.−1PX is the same as ▼(Choose one).
Solution
(a) The event X includes the outcomes 3, 4, 5, 6, 7, and 8. Since there are 8 equally sized slices and 6 of them are grey, the probability of X, PX, is 6/8 or 0.75.
The event not X includes the outcomes 1 and 2. Since there are 8 equally sized slices and 2 of them are white, the probability of not X, Pnot X, is 2/8 or 0.25.
Event Outcomes Probability 1 2 3 4 5 6 7 8 X ✓ ✓ ✓ ✓ ✓ =0.75 not X ✓ ✓ =0.25
(b) Subtracting Pnot X from PX gives 0.75 - 0.25 = 0.5.
(c) -1PX is the same as subtracting the probability of event X from 1. So, -1PX = 1 - PX = 1 - 0.75 = 0.25. This is the same as the probability of not X, Pnot X.
Similar Questions
A dartboard has 6 equally sized slices numbered from 1 to 6.Some are grey and some are white, as shown below.Answer the following questions. Write each answer as a fraction.A dart will be tossed and will land on a slice at random.(a) What is the probability that the dart lands on a grey slice?(b) What is the probability that the dart lands on a grey slice, given that the dart lands on an odd-numbered slice?
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).
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.
You throw two darts at a dartboard.Let event A = The first dart hits the center.Let event B = The second dart hits the center.What does P(B|A) represent?A.The probability that the first dart hits the center given that the second dart hits the centerB.The probability that the second dart hits the center given that the first dart hits the centerC.The probability that the second dart doesn't hit the centerD.The probability that either the first dart or the second dart hits the center
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
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.