11.4 Tree Diagrams 699 20. A New Home Theater System For your new home theater system you are going to purchase a media player, a receiver, and a speaker system at random from among the following brands. Media Player Receiver Speaker System LG Yamaha Bose Toshiba Onkyo JBL Sony Pioneer Insignia a) Determine the number of sample points in the sample space. 24 b) Construct a tree diagram and list the sample space. * Determine the probability of selecting c) a Sony media player. 1 4 d) Bose speakers. 1 2 e) a Sony media player and Bose speakers. 1 8 21. Landscaping The Franks just moved into a new home and need to do some landscaping. They are going to purchase one tree, one shrub, and one lilac bush at random from the list below. Trees Shrubs Lilac Bushes Dogwood Forsythia Common Maple Holly Sensation Birch Juniper Primrose a) Determine the number of sample points in the sample space. 27 b) Construct a tree diagram and list the sample space. * Determine the probability that the Franks select c) a maple tree. 1 3 d) a dogwood tree and a holly shrub. 1 9 e) a lilac bush other than Sensation. 2 3 22. Literature Choices You decide to take a literature course. A requirement for the course is that you must read one classic book, one nonfiction book, and one science fiction book from the list below. Classic Nonfiction Science Fiction Ficciones (F) Go Tell It on the Mountain (G) Tom Sawyer (T) Moby-Dick (M) John Adams (J) Angela’s Ashes (A) Dune (D) Ender’s Game (E) If the books are randomly selected, a) determine the number of sample points in the sample space. 16 b) construct a tree diagram and list the sample space. * Determine the probability that c) John Adams is selected. 1 2 d) either Ficciones or Tom Sawyer is selected. 1 2 e) Moby-Dick is not selected. 3 4 23. Clothing Options Brisson is getting dressed for work and is considering his options for a shirt, a tie, and a pair of slacks to wear. He has shirts available in white, pink, and yellow. He has ties available in red, blue and gray. He has pairs of slacks available in navy and khaki. a) How many different options for a shirt, a tie, and a pair of slacks does Brisson have? 18 b) Construct a tree diagram and list the sample space. * Assuming all options are equally likely, what is the probability that Brisson chooses c) a white shirt, a red tie, and a navy pair of slacks? 1 18 d) a gray tie? 1 3 e) a shirt other than a white shirt? 2 3 24. Mendel Revisited A pea plant must have exactly one of each of the following pairs of traits: short s( ) or tall t( ); round r( ) or wrinkled w( ) seeds; yellow y( ) or green g( ) peas; and white wh ( ) or purple p( ) flowers (for example, short, wrinkled, green pea with white flowers). a) How many different classifications of pea plants are possible? 16 b) Use a tree diagram to list all the classifications possible. * If each characteristic is equally likely c) determine the probability that the pea plant will have round peas. 1 2 d) determine the probability that the pea plant will be short, have wrinkled seeds, have yellow seeds, and have purple flowers. 1 16 *See Instructor Answer Appendix Gareth Boden/Pearson Education Ltd
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