700 CHAPTER 11 Probability 25. Coin Toss Odds Three coins are tossed. a) Construct a tree diagram and list the sample space. * b) Determine the odds against tossing all heads. 7 : 1 c) Determine the odds against tossing no heads. 7 : 1 d) Determine the odds against tossing at least one head. 1 : 7 e) Determine the odds against tossing at least two heads. 1 : 1 26. Golf Balls Atticus has 4 golf balls in his bag. The brand names on these golf balls are Callaway, Nitro, Titleist, and Wilson. Atticus randomly selects two golf balls, without replacement, from his bag. a) Construct a tree diagram and list the sample space. * b) Determine the odds against selecting a Callaway and a Titleist (in either order). 5 : 1 c) Determine the odds against selecting a Nitro. 1 : 1 d) Determine the odds against selecting no Wilsons. 1 : 1 e) Determine the odds against selecting a Callaway or a Wilson. 1 : 5 Challenge Problems/Group Activities 27. Three Chips Suppose that a bag contains one white chip and two red chips. Two chips are going to be randomly selected from the bag with replacement. a) What is the probability of selecting a white chip from the bag on the first selection? 1 3 b) What are the odds against selecting a white chip from the bag on the first selection? 2 : 1 c) What is the probability of selecting a red chip from the bag on the first selection? 2 3 d) Are the outcomes of selecting a white chip and selecting a red chip on the first selection equally likely? Explain. * e) The sample space when two chips are selected from the bag with replacement is ww, wr, rw, rr. Do you believe that the probability of selecting ww is greater than, equal to, or less than the probability of selecting rr? Explain. Answers will vary. 28. Thumbtacks A thumbtack is dropped on a concrete floor. Assume that the thumbtack can land only point up (u) or point down (d), as shown below. If two thumbtacks are dropped, one after the other, the following tree diagram can be used to show the possible outcomes. a) Do you believe that the outcomes of the thumbtack landing point up and the thumbtack landing point down are equally likely? Explain. Answers will vary. b) List the sample points in the sample space of this experiment. uu, ud, du, dd c) Do you believe that the probability that both thumbtacks land point up uu ( ) is the same as the probability that both thumbtacks land point down dd ( )? Explain. Answers will vary. d) Can you compute the theoretical probability of a thumbtack landing point up and the theoretical probability of a thumbtack landing point down? Explain. It is not possible; answers as to why it is not possible will vary. e) Obtain a box of thumbtacks and drop the thumbtacks out of the box. Determine the empirical probability of a thumbtack landing point up when dropped and the empirical probability of a thumbtack landing point down when dropped. Answers will vary. Recreational Mathematics 29. Ties All my ties are red except two. All my ties are blue except two. All my ties are brown except two. How many ties do I have? 3; 1 red, 1 blue, and 1 brown 30. Rock Faces An experiment consists of 3 parts: tossing a coin, tossing a rock, and rolling a die. If the sample space consists of 60 sample points, determine the number of faces on the rock. 5 faces JUMBLE For Exercises 31 and 32, refer to the Recreational Math box on page 693. Determine a) the number of possible arrangements of the letters given. b) the word when the letters are placed in the proper order. 31. ROTES a) 120 b) STORE 32. STEABK a) 720 b) BASKET u u d d d u First Thumbtack Second Thumbtack *See Instructor Answer Appendix
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