• Prove that if E and F are events in a sample space S (not necessarily finite) such that E C F, and p is a probability on S, then indeed p(E) < p(F).
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- A wheel has 10 equally sized slices numbered from 1 to 10. Some are grey and some are white. The slices numbered 1, 2, and 6 are grey. The slices numbered 3, 4, 5, 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 P (X) be the probability of X. Let not X be the event that the wheel stops on a slice that is not white, and let P (not X) be the probability of not X. Event X not X Outcomes 1 2 3 4 5 6 7 8 9 10 0 U U (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. 0 □ Probability P(X) = P (not X) = 010 9 8 X 7 101 65 2 Ś 3 4P is a probability distribution on a sample space Ω, and let A, B ⊆ Ω be events with P(A) = 0.6 and P(B) = 0.7. Show that 0.1 ≤ P(B\A) ≤ 0.4.23
- A dartboard has 5 equally sized slices numbered from 1 to 5 .Some are grey and some are white.The slices numbered 2 , 3 , and 4 are grey.The slices numbered 1 and 5 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 P not 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 Probability 1 2 3 4 5 X =PX not X =PnotX (b)Subtract. =−1PX (c)Select the answer that makes the sentence true.…K Suppose that there is a white um containing four white balls and two red balls and there is a red urn containing two white balls and three red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red. For this problem, assume that OA. 5 represents drawing a white ball from an um and that R represents drawing a red ball from an urn. Draw a tree diagram that represents this situation. Choose the correct answer below. OD So, the probability of the second ball being red is (Type an integer or a simplified fraction.) OB. X OC. -RA company prices it's tornado insurance using the following assumptions: in any calendar year there can be at most one tornado in any calendar year the probability of a tornado is 0.15 The number of tornadoes in any calendar year is independent of the number of tornadoes in any other calendar year using the companies assumptions calculate the possibilities that there are fewer than 2 tornadoes in a 20 year.
- Suppose that an employee arrives late 15% of the time, leaves early 25% of the time, and both arrives late and leaves early 5% of the time. What is the probability that on a given day that employee will either arrive late or leave early (or both)? O 0.35 O 0.25 O None of these O 0.45b. Fewer than 3 of these cardholders over age 50 will dispute a t gailel. 18 Records of a credit card company show that 30% of its cardholders over age 50 dispute one or more charges on their statements during the year. is selected. probability that: A random sample of 10 cardholders over age 50 Assuming the records are correct, find the a. Exactly 3 of these cardholders over age 50 will dispute a charge during the coming year, 10/3- charge during the coming year,Five balls numbered from 1 to 5 are placed into a bag. Some are grey and some are white. The ball numbered 1 is grey. The balls numbered 2, 3, 4, and 5 are white. A ball is selected at random. Let X be the event that the selected ball is white, and let P(X) be the probability of 12345 X. Let not X be the event that the selected ball is not white, and let P (not X) be the probability of not X. 4 (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. Aa Outcomes Event Probability 1 2 3 4 5 X OOOOO P(X) = not X P (not X) = (b) Subtract. C O O 1- P(x) = (c) Select the answer that makes the sentence true. 1-P(X) is the same as (Choose one) 00 S C. X ? &圖
- A dartboard has 5 equally sized slices numbered from 1 to 5. Some are grey and some are white. 5 1 The slices numbered 3 and 4 are grey. The slices numbered 1, 2, and 5 are white. 4 2 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 P (X) be the probability of X. Let not X be the event that the dart lands on a slice that is not grey, and let P (not 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. Outcomes Event Probability 123 4 5 ? O000O P(x) = ] 미미미미미 P(not X) = □ not X (b) Subtract. 1 - P(x) = [] (c) Select the answer that makes the sentence true. 1-P(X) is the same as (Choose one) 3. olo XTen bal nbered from 1 to 10 are placed into a bag. Some a. y ey and some are white. The ball numbered 3 is grey. The balls numbered 1, 2, 4, 5, 6, 7, 8, 9, and 10 are white. A ball is selected at random. Let X be the event that the selected ball is white, and let P(X) be the probability of X. Let not X be the event that the selected ball is not white, and let P (not 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. Outcomes Event Probability 1 2|3 4 5 6 789 10 O000 Olo P(x) = 0 not X Oln P(пot X) - П oloSuppose identical tags are placed on both the left ear and the right ear of a fox. The fox is then left loose for a period of time. Consider the two events C1 = { left ear tag is lost } and C2 = { right ear tag is lost }. Let π = P(C1) = P(C2), and assume C1 and C2 are independent events. Derive an expression (π ) for the probability that exactly one tag is lost, given that at most one is lost ( " Ear Tag Loss in Red Foxes," J. Wildlife Mgmt., 1976: 164-167). [ Hint : Draw a tree diagram in which the two initial branches refer to whether the left ear tag was lost.]
