SECTION 13.3 Probability 933 24. Which of the assignments of probabilities should be used if the coin is known to be fair? 25. Which of the assignments of probabilities should be used if the coin is known to always come up tails? 26. Which of the assignments of probabilities should be used if tails is twice as likely as heads to occur? 27. Assigning Probabilities A coin is weighted so that heads is four times as likely as tails to occur. What probability should be assigned to heads? to tails? 28. Assigning Probabilities A coin is weighted so that tails is twice as likely as heads to occur. What probability should be assigned to heads? to tails? 29. Assigning Probabilities A die is weighted so that an odd-numbered face is twice as likely to occur as an even-numbered face. What probability should be assigned to each face? 30. Assigning Probabilities A die is weighted so that a six cannot appear. All the other faces occur with the same probability. What probability should be assigned to each face? For Problems 31–34, the sample space is { = S 1, 2, 3, 4, 5, 6, } 7, 8, 9, 10 . Suppose that the outcomes are equally likely. 31. Compute the probability of the event { } = E 1, 2, 3 . 32. Compute the probability of the event { } = F 3, 5, 9, 10 . 33. Compute the probability of the event E: “an even number.” 34. Compute the probability of the event F: “an odd number.” For Problems 35 and 36, an urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles. 35. If one marble is selected, determine the probability that it is white. 36. If one marble is selected, determine the probability that it is black. In Problems 37–40, assume equally likely outcomes. 37. Determine the probability of having 3 boys in a 3-child family. 38. Determine the probability of having 3 girls in a 3-child family. 39. Determine the probability of having 1 girl and 3 boys in a 4-child family. 40. Determine the probability of having 2 girls and 2 boys in a 4-child family. For Problems 41–44, two fair dice are rolled. 41. Determine the probability that the sum of the faces is 7. 42. Determine the probability that the sum of the faces is 11. 43. Determine the probability that the sum of the faces is 3. 44. Determine the probability that the sum of the faces is 12. In Problems 45–48, find the probability of the indicated event if ( ) = P A 0.25 and ( ) = P B 0.45. 45. ( ) ∪ P A B if ( ) ∩ = P A B 0.15 46. ( ) ∩ P A B if ( ) ∪ = P A B 0.6 In Problems 11–16, (a) list the sample space S of each experiment and (b) construct a probability model for the experiment. 11. Tossing a fair coin twice 12. Tossing two fair coins once 13. Tossing two fair coins and then a fair die 14. Tossing a fair coin, a fair die, and then a fair coin 15. Tossing three fair coins once 16. Tossing one fair coin three times In Problems 17–22, use the following spinners to construct a probability model for each experiment. 2 1 4 Spinner I (4 equal areas) 3 Yellow Red Green Spinner II (3 equal areas) Forward Backward Spinner III (2 equal areas) 17. Spin spinner I, then spinner II. What is the probability of getting a 2 or a 4, followed by Red? 18. Spin spinner III, then spinner II. What is the probability of getting Forward, followed by Yellow or Green? 19. Spin spinner I, then II, then III. What is the probability of getting a 1, followed by Red or Green, followed by Backward? 20. Spin spinner II, then I, then III. What is the probability of getting Yellow, followed by a 2 or a 4, followed by Forward? 21. Spin spinner I twice, then spinner II. What is the probability of getting a 2, followed by a 2 or a 4, followed by Red or Green? 22. Spin spinner III, then spinner I twice.What is the probability of getting Forward, followed by a 1 or a 3, followed by a 2 or a 4? In Problems 23–26, consider the experiment of tossing a coin twice. The table lists six possible assignments of probabilities for this experiment. Using this table, answer the following questions. Assignments Sample Space HH HT TH TT A 1 4 1 4 1 4 1 4 B 0 0 0 1 C 3 16 5 16 5 16 3 16 D 1 2 1 2 − 1 2 1 2 E 1 4 1 4 1 4 1 8 F 1 9 2 9 2 9 4 9 23. Which of the assignments of probabilities is(are) consistent with the definition of a probability model?
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