#31,34,35,38,39,40,42

Section 5.2 Exercises 355 (a) What probability should replace "?" in the table? Why? (b) Find the probability that the chosen trip did not begin 42. Is this your card? A standard deck of playing cards (with between 9 A.M. and 12:59 P.M . jokers removed) consists of 52 cards in four suits- clubs, diamonds, hearts, and spades. Each suit has 13 cards, with 39. Education among young adults Choose a young adult denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, (aged 25 to 29) at random. The probability is 0.13 that the and king. The jacks, queens, and kings are referred to as person chosen did not complete high school, 0.29 that the "face cards." Imagine that we shuffle the deck thoroughly person has a high school diploma but no further education, and deal one card. Define events F: getting a face card, and 0.30 that the person has at least a bachelor's degree. and H: getting a heart. The two-way table summarizes the (a) What must be the probability that a randomly chosen sample space for this random process. young adult has some education beyond high school Card but does not have a bachelor's degree? Why? Face card Nonface card Total (b) Find the probability that the young adult completed Heart 10 13 high school. Which probability rule did you use to find Suit 3 the answer? Nonheart 9 30 39 Total 12 40 52 (c) Find the probability that the young adult has further education beyond high school. Which probability rule did you use to find the answer? (a) Find P(HC). 0. Preparing for the GMAT A company that offers courses b) Find P(H and F). Interpret this value in context. to prepare students for the Graduate Management (c) Find P(HC or F). Admission Test (GMAT) has collected the following information about its customers: 20% are undergraduate 43. Cell phones The Pew Research Center asked a random students in business, 15% are undergraduate students in sample of 2024 adult cell-phone owners from the United other fields of study, and 60% are college graduates who States their age and which type of cell phone they own: iPhone, Android, or other (including non-smartphones). are currently employed. Choose a customer at random. The two-way table summarizes the data. (a) What must be the probability that the customer is a college graduate who is not currently employed? Why? Age (b) Find the probability that the customer is currently an 18-34 35-54 55+ Total undergraduate. Which probability rule did you use to Phone 169 171 127 167 find the answer? Type of cell Android 214 189 100 503 phone (c) Find the probability that the customer is not an Other 134 277 643 1054 undergraduate business student. Which probability Total 517 637 870 2024 rule did you use to find the answer? 41. Who eats breakfast? Students in an urban school Suppose we select one of the survey respondents at i were curious about how many children regularly eat random. What's the probability that: breakfast. They conducted a survey, asking, "Do you (a) The person is not age 18 to 34 and does not own an eat breakfast on a regular basis?" All 595 students in the iPhone? school responded to the survey. The resulting data are shown in the two-way table. (b) The person is age 18 to 34 or owns an iPhone? Gender 44. Middle school values Researchers carried out a survey Male Female Total of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic Eats breakfast 190 110 300 ability, or being popular was most important to them. No 130 165 295 The two-way table summarizes the survey data." Total 320 275 595 Suppose we select a student from the school at random, Grade Define event F as getting a female student and event B 4th grade 5th grade | 6th grade | Total as getting a student who eats breakfast regularly. Grades 50 69 168 (a) Find PUBS). Most Athletic 24 38 important (by Find P(F and By Interpret this value in context, Popular 19 22 28 92 108 (c) Find P(F or B) Total 135 335354 CHAPTER 5 PROBABILITY Section 5.2 Exercises (a) Explain why this is a valid probability model. 31. Four-sided dice A four-sided die is a pyramid whose pg1343 four faces are labeled with the numbers 1, 2, 3, and 4 (b) Find the probability that a student does not win extra (see image). Imagine rolling two fair, four-sided dice homework. and recording the number that is showing at the base of ) What's the probability that a student wins candy or a each pyramid. For instance, you would record a 4 if the homework pass? die landed as shown in the figure. 36. Languages in Canada Canada has two official languages, English and French. Choose a Canadian at random and ask, "What is your mother tongue?" Here is the distribution of responses, combining many separate languages from the broad Asia/Pacific region:6 French Asian/Pacific Language English Other Probability 0.63 0.22 0.06 0.09 (a) Give a probability model for this random process. (b) Define event A as getting a sum of 5. Find P(A). (a) Explain why this is a valid probability model 32. Tossing coins Imagine tossing a fair coin 3 times. (b) What is the probability that the chosen person's mother tongue is not English? (a) Give a probability model for this random process. (c) What is the probability that the chosen person's mother (b) Define event B as getting more heads than tails. Find tongue is one of Canada's official languages? P(B). 37. Household size In government data, a household 33. Grandkids Mr. Starnes and his wife have 6 grand- children: Connor, Declan, Lucas, Piper, Sedona, and consists of all occupants of a dwelling unit. Choose an Zayne. They have 2 extra tickets to a holiday show, and American household at random and count the number will randomly select which 2 grandkids get to see the of people it contains. Here is the assignment of proba- show with them. bilities for the outcome. The probability of finding 3 people in a household is the same as the probability (a) Give a probability model for this random process. of finding 4 people. b) Find the probability that at least one of the two girls Number of people 1 2 3 4 5 6 7+ (Piper and Sedona) get to go to the show. Probability 0.25 0.32 0.07 0.03 0.01 34. Who's paying? Abigail, Bobby, Carlos, DeAnna, and Emily go to the bagel shop for lunch every Thursday. a) What probability should replace "?" in the table? Each time, they randomly pick 2 of the group to pay Why? for lunch by drawing names from a hat. (b) Find the probability that the chosen household (a) Give a probability model for this random process. contains more than 2 people. (b) Find the probability that Carlos or DeAnna (or both) ends up paying for lunch. 38. When did you leave? The National Household Travel Survey gathers data on the time of day when people 35. Mystery box Ms. Tyson keeps a Mystery Box in her begin a trip in their car or other vehicle. Choose a pg1345 classroom. If a student meets expectations for behavior, trip at random and record the time at which the trip she or he is allowed to draw a slip of paper without started. Here is an assignment of probabilities for the looking. The slips are all of equal size, are well mixed, outcomes: and have the name of a prize written on them. One of the "prizes"- extra homework - isn't very desirable! Time of day 10 P.M.-12:59 A.M. 1 A.M.-5:59 A.M. 6 A.M.-8:59 AM. Here is the probability model for the prizes a student Probability .040 0.033 3.144 can win: Time of day 9 A.M.-12:59 P.M. 1 P.M.-3:59 P.M. 4 P.M.-6:59 P.M. Prize Probability Pencil Candy Stickers Homework pass Extra homework 0.234 0.208 Probability 0.40 0.25 0.15 Time of day 0.15 7 P.M.-9:59 P.M. 0.05 Probability 0.123