#43,46,47,50,51,53,54

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 335356 CHAPTER 5 PROBABILITY (b) Find P(R) and P(N) Suppose we select one of these students at random. (c) Describe the event "R and N" in words. Then find the What's the probability of each of the following probability of this event. (a) The student is a sixth-grader or rated good grades as d) Explain why P(R or N) - P(R) + P(N). Then use the important. general addition rule to compute P(R or N). (b) The student is not a sixth-grader and did not rate good Dogs and cats In one large city. 40% of all household grades as important. ORA own a dog, 32% own a cat, and 18% own both. Sup 45. Roulette An American roulette wheel has 38 slots pose we randomly select a household. What's the prob with numbers I through 36, 0, and 00, as shown in ability that the household owns a dog or a cat? the figure. Of the numbered slots, 18 are ted, 18 are black, and 2-the 0 and 00-are green, When 48. Reading the paper In a large business hotel, 40% the wheel is spun, a metal ball is dropped onto the of guests read the Los Angeles Times. Only 25% middle of the wheel. If the wheel is balanced, the read the Wall Street Journal. Five percent of guests ball is equally likely to settle in any of the numbered read both papers. Suppose we select a ho slots. Imagine spinning a fair wheel once. Define at random and record which of the two papers the events B: ball lands in a black slot, and E: ball lands person reads, if either. What's the probability that in an even-numbered slot. (Treat 0 and 00 as even the person reads the Los Angeles Times or the Wall numbers.) Street Journal? 49. Mac or PC? A recent census at a major university revealed that 60% of its students mainly used Macs. The rest mainly used PCs. At the time of the census, 67% of the school's students were undergraduates. O The rest were graduate students. In the census, 23% of respondents were graduate students and used a Mac as their main computer. Suppose we select a student at random from among those who were part of the census. Define events G: is a graduate student, and M: primarily uses a Mac. (a) Find P(G U M). Interpret this value in context. (b) Consider the event that the randomly selected stu- dent is an undergraduate student and primarily uses a PC. Write this event in symbolic form and find its probability. (a) Make a two-way table that displays the sample space in 50. Gender and political party In January 2017, 52% of terms of events B and E. U.S. senators were Republicans and the rest were Dem- (b) Find P(B) and P(E). ocrats or Independents. Twenty-one percent of the sen- (c) Describe the event "B and E" in words. Then find the ators were females, and 47% of the senators were male probability of this event. Republicans. Suppose we select one of these senators (d) Explain why P(B or E) = P(B) + P(E). Then use the male. at random. Define events R: is a Republican, and M: is general addition rule to compute P(B or E). (a) Find P(R UM). Interpret this value in context. 46. Colorful disks A jar contains 36 disks: 9 each of four colors-red, green, blue, and yellow. Each set of b) Consider the event that the randomly selected senator disks of the same color is numbered from 1 to 9. is a female Democrat or Independent. Write this event Suppose you draw one disk at random from the jar. in symbolic form and find its probability. Define events R: get a red disk, and N: get a disk with the number 9. 51. Dogs and cats Refer to Exercise 47. (a) Make a two-way table that describes the sample space (a) Make a Venn diagram to display the outcomes of this in terms of events R and N. pg 352 random process using events D: owns a dog and C: owns a cat. (b) Find P(Dn CC).Section 5.2 Exercises 357 52. Reading the paper Refer to Exercise 48. (a) Make a Venn diagram to display the outcomes of this Recycle and Review random process using events L: reads the Los Angeles 59. Crawl before you walk (3.1, 3.2, 4.3) At what age do Times and W: reads the Wall Street Journal. babies learn to crawl? Does it take longer to learn in (b ) Find P ( LC n w). the winter, when babies are often bundled in clothes that restrict their movement? Perhaps there might even 53. Union and intersection Suppose A and B are be an association between babies' crawling age and two events such that P(A) = 0.3, P(B) = 0.4, and the average temperature during the month they first P(A UB) = 0.58. Find P(AnB). try to crawl (around 6 months after birth). Data were collected from parents who brought their babies to the 54. Union and intersection Suppose C and D are University of Denver Infant Study Center to participate two events such that P(C) = 0.6, P(D) = 0.45, and in one of a number of studies. Parents reported the P(CUD) = 0.75. Find P(CnD). birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within one Multiple Choice: Select the best answer for Exercises 55-58. minute. Information was obtained on 414 infants (208 55. The partially completed table that follows shows the boys and 206 girls). Crawling age is given in weeks, and distribution of scores on the 2016 AP Statistics exam. average temperature (in degrees Fahrenheit) is given for the month that is 6 months after the birth month. 10 Score 1 2 3 Birth month Average crawling age Average temperature Probability 0.235 0.155 0.249 0.217 January 29.84 66 Suppose we randomly select a student who took this February 30.52 73 exam. What's the probability that he or she earned a March 29.70 72 score of at least 3? April 31.84 63 (a) 0.249 (b) 0.361 (c) 0.390 May 28.58 52 (d) 0.466 (e) 0.610 June 31.44 39 56. In a sample of 275 students, 20 say they are vegetarians. July 33.64 33 Of the vegetarians, 9 eat both fish and eggs, 3 eat eggs August 32.82 30 but not fish, I eats fish but not eggs, and 7 eat neither. September 33.83 33 Choose one of the vegetarians at random. What is the October 33.35 37 probability that the chosen student eats fish or eggs? November 33.38 48 (a) 9/20 (b) 13/20 (c) 22/20 December 32.32 57 (d) 9/275 (e) 22/275 (a) Make an appropriate graph to display the relationship Exercises 57 and 58 refer to the following setting. The casino between average temperature and average crawling game craps is based on rolling two dice. Here is the assign- age. Describe what you see. ment of probabilities to the sum of the numbers on the Some computer output from a linear regression analysis up-faces when two dice are rolled: of the data is shown. Coef SE Coef T-Value P-Value Outcome 2 3 5 6 7 8 9 10 11 12 Term Probability 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36 Constant 35 . 68 1. 32 27. 08 0 . 000 $7. The most common bet in craps is the "pass line." A Average -0.0777 0. 0251 -3 . 10 0. 011 pass line bettor wins immediately if either a 7 or an temperature 11 comes up on the first roll. This is called a natural. S = 1.31920 R-Sq = 48.968 R-Sq(adj ) = 43 . 868 What is the probability that a natural does not occur? (b) What is the equation of the least-squares regression (a) 2/36 ( b) 6/36 (c) 8/36 line that describes the relationship between average d) 16/36 (e) 28/36 temperature and average crawling age? Define any 38. If a player rolls a 2, 3, or 12, it is called craps. What is variables that you use. the probability of getting craps or an even sum on one (c) Interpret the slope of the regression line. roll of the dice? (d) Can we conclude that warmer temperatures 6 months (a) 4/36 (b) 18/36 (c) 20/36 after babies are born causes them to crawl sooner? (d) 22/36 Justify your answer. (e ) 32/36