'3\"? map 4.111 New England Patriots. From the National Football League (NFL) Web site, in the New England Patriots Roster, we obtained information on the weights and years of experience for the players on that team, as of September 26, 2013. The following contingency table provides a cross-classication of those data. Years of experience Rookie 15 610 Over 10 Y1 72 Y3 Y4 Total Under 200 W] 3 5 Over 300 W3 -n-4-5- Weight (lb) How many cells are in this contingency table? . How many players are on the New England Patriots roster as of September 26, 2013? How many players are rookies? . How many players weigh between 200 and 300 lb? . How many players are rookies who weigh between 200 and 300 lb? son-99'? '."' Tenure of operator Full Part OWI'ICI' owner Tenant T3 Total I: '5'] 50Lunder 180 A2 492 130 38 \"a"; I ISOunder 500 g A3 198 368 500under 1000 A 51 14 149 4 1000 & over 114 .t x] 172 1521 541 .L Fill in the six missing entn'es. How many cells does this contingency table have? How many farms have under 50 acres? . How many farms are tenant operated? How many farms are operated by part owners and have be- tween 500 and 1000 acres? How many farms are not full-owner operated? g. How many tenant-operated farms have 180 acres or more? 4.114 Farms. The US. Department of Agriculture publishes infor~ mation about US. farms in C ensus of A gricuimre. A joint frequency distribution for number of farms, by acreage and tenure of operator, is provided in the following contingency table. Frequencies are in thousands. Tenure of operator Full Part owner owner Tenant T1 T2 T3 Total Under 50 A 70 44 l SOLunder 180 A 492 130 38 2 3' as ISOunder 500 _ g A3 368 4: 5 1 14 149 A4 1000 & over 41 1 l4 17 172 Fill in the six missing entries. How many cells does this contingency table have? How many farms have under 50 acres? . How many farms are tenant operated? How many farms are operated by part owners and have be tween 500 and 1000 acres? 99-??? 4.14 Playing Cards. An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs- with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is a. a spade? b. red? c. not a club? 4.17 Russian Presidential Election. According to the Central Election Commission of the Russian Federation, a frequency distribu- tion for the March 4, 2012 Russian presidential election is as follows. Candidate Votes Vladimir Putin 45,513,001 Gennady Zyuganov 12,288,624 Mikhail Prokhorov 5,680,558 Vladimir Zhirinovsky 4,448,959 Sergey Mironov 2,755,642 Find the probability that a randomly selected voter voted for a. Putin. b. either Zhirinovsky or Mironov. c. someone other than Putin.4.24 Family Size. A family is dened to be a group of two or more persons related by birth, marriage, or adaption and residing together in a household. According to Current Population Survey, published by the U.S. Census Bureau, the size distribution of U.S. families is as follows. Frequencies are in thousands. A U.S. family is selected at random. Find the probability that the family obtained has a. two persons. b. more than three persons. c. between one and three persons, inclusive. d. one person. e. one or more persons. Section 4.2 and 4.3 4.55 Committee Selection. A committee consists of five execu- tives, three women and two men. Their names are Maria (M), John (J), Susan (S), Will (W), and Holly (H). The committee needs to select a chairperson and a secretary. It decides to make the selection ran- domly by drawing straws. The person getting the longest straw will be appointed chairperson, and the one getting the shortest straw will be appointed secretary. The possible outcomes can be represented in the following manner. MS SM HM JM WM MH SH HS JS WS MJ SJ HJ JH WH MW SW HW JW WJ Here, for example, MS represents the outcome that Maria is appointed chairperson and Susan is appointed secretary. List the outcomes con- stituting each of the following four events. A = event a male is appointed chairperson, B = event Holly is appointed chairperson, C = event Will is appointed secretary, D = event only females are appointed.4.56 Coin Tossing. When a dime is tossed four times, there are the following 16 possible outcomes. HHHH HTHH THHH TTHH HHHT HTHT THHT TTHT HHTH HTTH THTH TTTH HHTT HTTT THTT TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes constituting each of the following four events. A = event exactly two heads are tossed, B = event the first two tosses are tails, C = event the first toss is heads, D = event all four tosses come up the same.4.91 Internet Access. From the document \"Computer and Internet Use in the United States: Population Characteristics\" (Current Popu- lation S away) by T. File, we obtained the following percentage distri- bution of household income for U.S. households with Internet access. Household income Event Less than $25,000 A $25,000$49,999 B $50,000S99,999 C $100,000$ 149,999 D $150,000 or more E Suppose that a U.S. household with Internet access is selected at random. Let A denote the event that the household has an income under $25,000, B denote the event that the household has an income between $25,000 and $49,999, and so on (see the third column of the table). Apply the special addition rule to nd the probability that the household obtained has an income under $50,000. $25,000 or above. between $25,000 and $149,999, inclusive. . Interpret each of your answers in parts (a)(c) in terms of percentages. a??? 4.95 Student Debt. The Association of American Universities pub- lished a report titled \"Looking More Closely at Student Debt.\" This report explores the issue about the cost of a college education and its impact on student loan debt. Using information from a credit report- ing company, the following table provides a percentage distribution for the loan balance of outstanding student loans from individuals with graduate, professional, and undergraduate degree debt. Loan balance Percentage $1$10.000 43.1 $10,001$25,000 29.2 $25,001 $50,000 16.5 $50,001$75,000 5.8 $75,001$100,000 2.3 $100,001 or more 3.1 Suppose that one of these individuals is selected at random. a. Without using the general addition rule, determine the probabil- ity that the individual obtained has a loan balance either between $10,001 and $100,000, inclusive, or at most $75,000. b. Obtain the probability in part (a) by using the general addition rule. c. Which method did you nd easier? 4.97 Craps. In the game of craps, a player rolls two balanced dice. Thirty-six equally likely outcomes are possible, as shown in Fig. 4.1 on page 159. Let A = event the sum of the dice is 7, B = event the sum of the dice is l l, C = event the sum of the dice is 2, D = event the sum of the dice is 3, E = event the sum of the dice is 12, F = event the sum of the dice is 8, and G = event doubles are rolled. a. Compute the probability of each of the seven events. b. The player wins on the rst roll if the sum of the dice is 7 or 11. Find the probability of that event by using the special addition rule and your answers from part (a). c. The player loses on the rst roll if the sum of the dice is 2, 3, or 12. Determine the probability of that event by using the special addition rule and your answers from part (a). d. Compute the probability that either the sum of the dice is 8 or doubles are rolled, without using the general addition rule. e. Compute the probability that either the sum of the dice is 8 01' doubles are rolled by using the general addition rule, and com- pare your answer to the one you obtained in part ((1)