8:31 PM Fri Jun 17 96% webassign.net 12. [-/1.07 Points] DETAILS ASWSBE14 4.E.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Refer to the KP&L sample points and sample point probabilities in the following tables. Completion Results for 40 KP&L Projects Completion Time (months) Number of Past Projects Stage 1 Stage 2 Sample Having These Design Construction Point Completion Times 2 6 (2, 6) 6 2 (2, 7 ) 2 2 8 (2, 8) 6 3 6 (3, 6) 4 3 (3, 7) 6 3 8 (3, 8 2 4 6 (4, 6) 2 4 7 (4, 7 ) 4 4 8 (4, 8) 8 Total: 40 Probability Assignments for the KP&L Project Based on the Relative Frequency Method Sample Project Probability of Point Completion Time Sample Point (2, 6) 8 months P(2, 6) = 6 = 0.15 40 ( 2, 7 ) 9 months P(2, 7) = 2 = 0.05 40 (2, 8 ) 10 months P(2, 8) = 6 = 0.15 40 (3, 6) 9 months P(3, 6) = 4 = 0.10 40 (3, 7) 10 months P(3, 7) = 6 = 0.15 40 (3, 8) 11 months P(3, 8) = 2 = 0.05 40 (4, 6) 10 months P(4, 6) = 2 = 0.05 40 ( 4, 7 ) 11 months P (4, 7) = 4 = 0.10 40 (4, 8) 12 months P(4, 8) = 8 = 0.20 408:30 PM Fri Jun 17 '5" 96%E} webassignnet 10. [-I1 .07 Points] DETAILS ASWSBE14 4.E.O15. MY NOTES ASK YOUR TEACH ER PRACTICE ANOTHER Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a Siz probability. (a) List the sample points in the event a queen is selected. 0 S = {12 of clubs, 12 of diamonds, 12 of hearts, 12 of spades} O S = {x | X is a card from the deck but not king, ace, or jack} 0 S = {queen of clubs, queen of diamonds, queen of hearts, queen of spades} O S = {x | x is a card from the deck that is not a diamond a heart or a club} 0 S = {king of clubs, king of diamonds, king of hearts, king of spades} (b) List the sample points in the event a diamond is selected. 0 S = {2 of diamonds, 3 of diamonds, ..., 10 of diamonds, jack of diamonds, queen of diamonds, king of diamonds, ace of diamonds} O S = {x | x is a card from the deck but not a club or a spade} O S = {1 of diamonds, 2 of diamonds, ..., 10 of diamonds, 11 of diamonds, 12 of diamonds, 13 of diamonds} O S = {2 of diamonds, 3 of diamonds, ..., 9 of diamonds, 10 of diamonds, jack of diamonds, queen of diamonds, king of diamonds} O S = {2 of hearts, 3 of hearts, ..., 10 of hearts, jack of hearts, queen of hearts, king of hearts, ace of hearts} (c) List the sample points in the event a face card (jack, queen, or king) is selected. 0 S = {x | x is a card from the deck that is not numbered} 0 S = {jack of hearts, queen of spades, king of clubs} 0 S = {11 of clubs, 11 of diamonds, 11 of hearts, 11 of spades, 12 of clubs, 12 of diamonds, 12 of hearts, 12 of spades, 13 of clubs, 13 of diamonds, 13 of hearts, 13 of spades} O S = {jack of clubs, queen of clubs, king of clubs, jack of hearts, queen of hearts, king of hearts, jack of spades, queen of spades, king of spades, jack of clubs, queen of clubs, king of clubs} 0 S = {jack of clubs, jack of diamonds, jack of hearts, jack of spades, queen of clubs, queen of diamonds, queen of hearts, queen of spades, king of clubs, king of diamonds, king of hearts, king of spades} (d) Find the probabilities associated with each of the events in parts (a), (b), and (c). (Enter your probabilities as fractions.) Form: [:1 Forum [:1 w :1 Need Help? 11. [-11.07 Points] DETAILS ASWSBE14 4.E.O16. MY NOTES ASK YOUR TEACH ER PRACTICE ANOTHER Conslder the experlment of rolling a pair of dice. Suppose that we are Interested In the sum of the face values showing on the dice. (a) How many sample points are possible? (Hint: use the counting rule for multiple-step experiments.) :1 (b) List the sample points. There v to sum the face values of a pair of dice to 2. There v to sum the face values of a pair of dice to 3. There v to sum the face values of a pair of dice to 4. Than: I _nlnr+_ n In an um rhn fan: ualnpc nf a hair nf Him to I: 8:30 PM Fri Jun 17 '5" 96% E} E webassignnet comma-separated list. Enter three unspaced capital letters For each permutation.) : Need Help? _ 4. [I1 .07 Points] DETAILS ASWSBE14 4.E.004. MY NOTES ASK YOUR TEACHER Consider the experiment of tossing a coin three times. (Let H be head and T be tail.) (a) Develop a tree diagram for the experiment. Tree Diagram Description (D (b) List the experimental outcomes. (Select all that apply.) O(H) O(T. H. T) O(T) O(T. T. H) O(T. H) O(T. T. T) O(H. H) O(H. T. T. T) O(H. T) O(T. T. T. H) O(T. T) O(H. T. H. T) O(H. H. H) O(T. H. T. H) O(H. H. T) O(H. T. T. H) O(H. T. H) O(T. T. H. H) O(H. T. T) O(H. H. T. T) O(T. H. H) O(T. H. H. T) (c) What is the probability for each experimental outcome? Need Help? 8:30 PM Fri Jun 17 '5\" 96%E} webassignnet 1. [41.07 Points] DETAILS ASWSBE14 4.E.OO1.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER An experiment has three steps with six outcomes possible for the first step, four outcomes possible for the second step, and seven outcomes possible For the third step. How many experimental outcomes exist For the entire experiment? Need Help? 2. [-I1 .07 Points] DETAILS ASWSBE14 4.E.002. MY NOTES ASK YOUR TEACHER How many ways can three items be selected from a group of six items? :1 Use the letters A, B, C, D, E, and F to identify the items, and list each of the different combinations of three items. (Enter your answers as a comma-separated list. Enter three unspaced capital letters for each combination.) : Need Help? 3. [I1 .07 Points] DETAILS ASWSBE14 4.E.003. MY NOTES ASK YOUR TEACHER How many permutations of three items can be selected from a group of six? :1 Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F. (Enter your answers as a comma-separated list. Enter three unspaced capital letters For each permutation.) : Need Help? 4. [I1 .07 Points] DETAILS ASWSBE14 4.E.004. MY NOTES ASK YOUR TEACHER Consider the experiment of tossing a coin three times. (Let H be head and T be tail.) (a) Develop a tree diagram for the experiment. Tree Diagram Description 8:31 PM Fri Jun 17 '6" 95% C} E webassignnet 15. [41.07 Points] DETAILS ASWSBE14 4.E.023.M|. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose that we have a sample space S = {E11 E2, E3, E4, E5, 56, E7}, where E1: Ezr . . ., E7 denote the sample points. The following probability assignments apply: P(El) = 0.20, P(E2) = 0.25, P(E3) = 0.15, P(E4) = 0.10, P(E5) = 0.05, P(E6) = 0.20, and P(E7) = 0.05. Let A = {51: E4: Ea} B = {E21 E4: 57} C = {52, 53' 55' E7}. (3) Find pm, 9(5), and P(C). p... = [:1 p... = [:1 PIC) = (b) Find A u 3. (Enter your answer in set notation.) Find PM u B). me: (C) Find A n 8. (Enter your answer In set notation.) Find P(A n s). m . .. = :1 (d) Are events A and C mutually exclusive? They mutually exclusive. (e) Find BC. (Enter your answer in set notation.) Find mac). sci = [:1 Need Help? 16. [-11.07 Points] DETAILS ASWSBE14 4.E.023.M|.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. _utorial Exercise Suppose that we have a sample space S = {EV E7, E2, E4, E... E5, 5,}, where 5,, E7, . .., E7 denote the sample points. The 8:30 PM Fri Jun 17 96% webassign.net Need Help? Read It Watch It 5. [-/1.07 Points] DETAILS ASWSBE14 4.E.005. MY NOTES ASK YOUR TEACHER Suppose an experiment has five equally likely outcomes: F1, E2, E3: E4, Es. Assign probabilities to each outcome. P ( E1 ) = P(E2) = P(E3) = P(E4) = P(E5) = Show that the requirements in the equations O S P(E ) S 1 for all i and P ( E , ) + P ( E 2 ) + . . . + P ( E, ) = 1 are satisfied. P(E) = for / = 1, 2, 3, 4, 5. Therefore, we have that all five probabilities ---Select-- greater than or equal 0 and less than or equal to 1, and the sum of the five probabilities is What method did you use? subjective method classical method relative frequency method empirical method Need Help? Read It Submit Answer 6. [-/1.07 Points] DETAILS ASWSBE14 4.E.006. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER An experiment with three outcomes has been repeated 50 times, and it was learned that E, occurred 10 times, E2 occurred 14 times, and E3 occurred 26 times. Assign probabilities to the outcomes. P(E1 ) = P(E2) = P(E3) = What method did you use? O subjective method empirical method O relative frequency method classical method Need Help? Read It Watch It8230 PM Fri Jun 17 '5" 96%E} webassignnet 7. [-I1.07 Points] DETAILS ASWSBE14 4.E.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E1) = 0.10, P(E2) = 0.15, P(E3) = 0.35, and P(E4) = 0.35. Are these probability assignmenE valid? Explain. O Nor the probabilities do not sum to 1. 0 Yes, 0 s P(E,) s 1 for all f and the probabilities' sum is greater than 1. O No, the subjective method requires that all probabilities be equal. 0 Yes, 0 s P(l_=,) s 1 for all f and the probabilities' sum is less than 1. Need Help? 8. [41.07 Points] DETAILS ASWSBE14 4.E.009.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible? Need Help? 9. [I1 .07 Points] DETAILS ASWSBE14 4.E.014. MY NOTES ASK YOUR TEACH ER PRACTICE ANOTHER An experiment has four equally likely outcomes: E1, E2, E3, and E4. (a) What is the probability that E3 occurs? D (b) What is the probability that any two of the outcomes occur (e.g., E3 or E4)? U (c) What is the probability that any three of the outcomes occur (e.g., E1 or E3 or E4)? U Need Help? _' 10. [11.07 Points] DETAILS ASWSBE14 4.E.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 5:2 probability. (a) List the sample points in the event a queen is selected. 0 5 = {12 of clubs, 12 of diamonds, 12 of hearts, 12 of spades} O S = {x | x is a card from the deck but not king, ace, or jack} 8:31 PM Fri Jun 17 96% a webassign.net 12. [-/1.07 Points] DETAILS ASWSBE14 4.E.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Refer to the KP&L sample points and sample point probabilities in the following tables. Completion Results for 40 KP&L Projects Completion Time (months) Number of Past Projects Stage 1 Stage 2 Sample Having These Design Construction Point Completion Times 2 (2, 6) 6 2 V (2, 7 ) 2 2 8 (2, 8) 6 3 6 (3, 6) 4 3 (3, 7) 6 3 8 (3, 8 2 4 6 (4, 6) 2 4 7 (4, 7 ) 4 4 8 (4, 8) 8 Total: 40 Probability Assignments for the KP&L Project Based on the Relative Frequency Method Sample Project Probability of Point Completion Time Sample Point (2, 6) 8 months P(2, 6) = 6 = 0.15 40 ( 2, 7 ) 9 months P(2, 7) = 2 = 0.05 40 (2, 8 ) 10 months P(2, 8) = 6 = 0.15 40 (3, 6) 9 months P(3, 6) = 4 = 0.10 40 (3, 7) 10 months P(3, 7) = 6 = 0.15 40 (3, 8) 11 months P(3, 8) = 2 = 0.05 40 ( 4, 6 ) 10 months P(4, 6) = 2 = 0.05 40 ( 4, 7 ) 11 months P (4, 7) = 4 = 0.10 40 (4, 8) 12 months P(4, 8) = 8 = 0.20 408:31 PM Fri Jun 17 96% webassign.net (b) Find P(A U B). P(A U B ) = Are A and B mutually exclusive? They: ---Select--- v mutually exclusive. -Select--- V are are not Find P(AC) and P (CC ). P ( AC ) = P (C C ) = (d) Find A U BC. (Enter your answer in set notation.) A UBC = Find P(A U BC). P(A U BC) = (e) Find P(B U C). P(B U C) = Need Help? Read It Submit Answer 15. [-/1.07 Points] DETAILS ASWSBE14 4.E.023.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose that we have a sample space S = {E1, E2, E3, E4, Es, E6, E7), where E1, E2, . . ., E, denote the sample points. The following probability assignments apply: P(E,) = 0.20, P(E2) = 0.25, P(E3) = 0.15, P(E4) = 0.10, P(Es) = 0.05, P(E6) = 0.20, and P(E7) = 0.05. Let A = {E1, E4, E6) B = {E2, EAI E7} C = {E2, E3, Es, E7). (a) Find P(A), P(B), and P(C). P(A) = P (B ) = P(C ) = (b) Find A U B. (Enter your answer in set notation.) AUB = Find P(A U B).8:31 PM Fri Jun 17 '6\" 96%E} webassignnet 13. [-11.07 Points] DETAILS ASWSBE14 4.E.019.M|. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Do you think global warming will have an impact on you during your lifetime? A poll of 1,000 adults asked this question. Consider the responses by age groups shown below. (a) What is the probability that a respondent 1829 years of age thinks that global warming will not pose a serious threat during his/her lifetime? (Round your answer to four decimal places.) :J (b) What is the probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime? (Round your answer to four decimal places.) S (c) For a randomly selected respondent, what is the probability that a respondent answers yes? :1 (d) Based on the survey results, does there appear to be a difference between ages 1829 and 30+ regarding concern over global warming? 0 It appears that older respondents and younger respondents are equally concerned about global warming being a threat in their lifetime. 0 It appears that older respondents are more concerned about global warming being a threat in their lifetime than are younger respondents. 0 It appears that older respondents are less concerned about global warming being a threat In their lifetime than are younger respondents. 0 It appears that older respondents and younger respondents are mostly unsure about global warming being a threat In their lifetime. NeedHeIp? 14. [I1 .07 Points] DETAILS ASWSBE14 4.E.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose that we have a sample space with ve equally likely experimental outcomes: E1, E2, E3' E4, E5. Let A = {E21E3} B = {11 4} C = {El' E3, E5}. (3) Find PM), pus), and P(C). Pm =:J Pm =:J Pia) = 8:31 PM Fri Jun 17 '5" 96%E} webassignnet rrLJ w :1 Need Help? 11. [-I1.07 Points] DETAILS ASWSBE14 4.E.O16. MY NOTES ASK YOUR TEACH ER PRACTICE ANOTHER Consider the experiment of rolling a pair of dice. Suppose that we are Interested In the sum of the face values showing on the dice. (a) How many sample points are possible? (Hint: use the counting rule for multiple-step experiments.) B (b) List the sample points. 48l8l3t v to sum the face values of a pair of dice to 2. _| 3' l'D 3 There elect v to sum the face values of a pair of dice to 3. i elect v to sum the face values of a pair of dice to 4. _' 3 B I There elect v to sum the face values of a pair of dice to 5. There v to sum the face values of a pair of dice to 6. There to sum the face values of a pair of dice to 7. There v to sum the face values of a pair of dice to 8. There v to sum the face values of a pair of dice to 9. There to sum the face values of a pair of dlce to 10. There to sum the face values of a pair of dlce to 11. There to sum the face values of a pair of dice to 12. (c) What is the probability of obtaining a value of 9? D (d) What is the probability of obtaining a value of 9 or greater? D (e) Because each roll has six possible even values (2, 4, 6, 8, 10, and 12) and only ve possible odd values (3, 5, 7, 9, and 11), the dice should show even values more often than odd values. Do you agree with this statement? Explain. This statement -Select- 1' correct because P(odd) = [:] and P(even) = [:]. (f) What method did you use to assign the probabilities requested? 0 empirical method 0 relative frequency method 0 subjective method 0 classical method Need Help? _