SUPPLEMENTARY EXERCISES for ... - WH Freeman

Section 2 31given a legitimate assignment of probabilities to the eight teams in the conference? Explainyour answer.S4.10 A sociologist studying social mobility in Denmark finds that the probability that the sonof a lower-class father remains in the lower class is 0.46. What is the probability that the sonmoves to one of the higher classes?S4.11 Government data assign a single cause for each death that occurs in the United States.The data show that the probability is 0.45 that a randomly chosen death was due to cardiovascular(mainly heart) disease, and 0.22 that it was due to cancer. What is the probability thata death was due either to cardiovascular disease or to cancer? What is the probability that thedeath was due to some other cause?S4.12 Select a first-year college student at random and ask what his or her academic rank wasin high school. Here are the probabilities, based on proportions from a large sample survey offirst-year students:Rank Top 20% Second 20% Third 20% Fourth 20% Lowest 20%Probability 0.41 0.23 0.29 0.06 0.01(a) What is the sum of these probabilities? Why do you expect the sum to have this value?(b) What is the probability that a randomly chosen first-year college student was not in the top20% of his or her high school class?(c) What is the probability that a first-year student was in the top 40% in high school?(d) Now choose two first-year college students at random. What is the probability that bothwere in the top 20% of their high school classes?S4.13 Choose an American farm at random and measure its size in acres. Here are the probabilitiesthat the farm chosen falls in several acreage categories:Acres < 10 10–49 50–99 100–179 180–499 500–999 1000–1999 ≥ 2000Probability 0.09 0.20 0.15 0.16 0.22 0.09 0.05 0.04Let A be the event that the farm is less than 50 acres in size, and let B be the event that it is500 acres or more.(a) Find P (A) and P (B).(b) Describe A c in words and find P (A c ) by the complement rule.(c) Describe {A or B} in words and find its probability by the addition rule.S4.14 Choose an American worker at random and classify his or her occupation into one of thefollowing classes. These classes are used in government employment data.ABCDEFManagerial and professionalTechnical, sales, administrative supportService occupationsPrecision production, craft, and repairOperators, fabricators, and laborersFarming, forestry, and fishing