III.1. What’s the probability? If you have access to a printed copy, open your local Yellow Pages telephone directory to any page in the Business White Pages listing. Look at the last four digits of each telephone number, the digits that specify an individual number within an exchange given by the first three digits. Note the first of these four digits in each of the first 100 telephone numbers on the page.

If you don’t have access to a printed directory, you can use an online directory. Find an online directory with at least 100 different phone numbers. Look at the last four digits of each telephone number, the digits that specify an individual number within an exchange given by the first three digits. Note the first of these four digits in each of the first 100 telephone numbers in the directory.

One directory we found online was at http://education.ohio.gov/Contact/Phone-Directory. State government agencies often have directories with office phone numbers of employees.

III.2. Blood types. Choose a person at random and record his or her blood type. Here are the probabilities for each blood type:

III.3. Grades in an economics course. Indiana University posts the grade distributions for its courses online. Students in Economics 201 in the fall 2013 semester received 18% A’s, 8% A−’s, 7% B+’s, 16% B’s, 11% B−’s, 6% C+’s, 12% C’s, 4% C−’s, 3% D+’s, 6% D’s, 4% D−’s, and 6% F’s. Choose an Economics 201 student at random. The probabilities for the student’s grade are:

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III.4. Blood types. People with Type B blood can receive blood donations from other people with either Type B or Type O blood. Tyra has Type B blood. What is the probability that two or more of Tyra’s six close friends can donate blood to her? Using your work in Exercise III.2, simulate 10 repetitions and estimate this probability. (Your estimate from just 10 repetitions isn’t reliable, but you have shown in principle how to find the probability.)

III.5. Grades in an economics course. If you choose four students at random from all those who have taken the course described in Exercise III.3, what is the probability that all the students chosen got a B or better? Simulate 10 repetitions of this random choosing and use your results to estimate the probability. (Your estimate from only 10 repetitions isn’t reliable, but if you can do 10, you could do 10,000.) (Hint: See page 447.)

III.6. Grades in an economics course. Choose a student at random from the course described in Exercise III.3 and observe what grade that student earns (with A = 4, A− = 3.7, B+ = 3.3, B = 3.0, B− = 2.7, C+ = 2.3, C = 2.0, C− =1.7, D+ = 1.3, D = 1.0, D− = 0.7, and F = 0.0).

III.7. Dice. What is the expected number of spots observed in rolling a carefully balanced die once? (Hint: See page 467.)

III.8. Profit from a risky investment. Rotter Partners is planning a major investment. The amount of profit X is uncertain, but a probabilistic estimate gives the following distribution (in millions of dollars):

What is the expected value of the profit?

III.9. Poker. Deal a five-card poker hand from a shuffled deck. The probabilities of several types of hand are approximately as follows:

III.10. How much education? The Census Bureau gives this distribution of education for a randomly chosen American over 25 years old in 2014:

III.11. Language study. Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results:

III.12. Choosing at random. Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm’s public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness, the choice will be made by drawing two names from a hat. (This is an SRS of size 2.)

III.13. Languages in Canada. Canada has two official languages: English and French. Choose a resident of Quebec at random and ask, “What is your mother tongue?’’ Here is the distribution of responses, combining many separate languages from the province of Quebec:

III.14. Is college worth the cost? A September 29, 2015, Gallup poll asked recent college graduates (those who obtained their bachelor’s degree beginning in 2006) whether their education was worth the cost. Assume that the results of the poll accurately reflect the opinions of all recent college graduates. Here is the distribution of responses:

III.15. An IQ test. The Wechsler Adult Intelligence Scale (WAIS) is a common IQ test for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 100 and standard deviation 15. Use the 68–95–99.7 rule to answer these questions.

III.16. Worrying about crime. How much do Americans worry about crime and violence? Suppose that 40% of all adults worry a great deal about crime and violence. (According to sample surveys that ask this question, 40% is about right.) A polling firm chooses an SRS of 2400 people. If they do this many times, the percentage of the sample who say they worry a great deal will vary from sample to sample following a Normal distribution with mean 40% and standard deviation 1.0%. Use the 68–95–99.7 rule to answer these questions.

III.17. An IQ test (optional). Use the information in Exercise III.15 and Table B to find the probability that a randomly chosen person has a WAIS score of 112 or higher. (Hint: See pages 434–435.)

III.18. Worrying about crime (optional). Use the information in Exercise III.16 and Table B to find the probability that one sample misses the truth about the population by 2.5% or more. (This is the probability that the sample result is either less than 37.5% or greater than 42.5%.)

III.19. An IQ test (optional). How high must a person score on the WAIS test to be in the top 10% of all scores? Use the information in Exercise III.15 and Table B to answer this question. (Hint: See pages 434–435.)

III.20. Models, legitimate and not. A bridge deck contains 52 cards, four of each of the 13 face values ace, king, queen, jack, ten, nine, . . . , two. You deal a single card from such a deck and record the face value of the card dealt. Give an assignment of probabilities to the possible outcomes that should be correct if the deck is thoroughly shuffled. Give a second assignment of probabilities that is legitimate (that is, obeys the rules of probability) but differs from your first choice. Then give a third assignment of probabilities that is not legitimate, and explain what is wrong with this choice.

III.21. Mendel’s peas. Gregor Mendel used garden peas in some of the experiments that revealed that inheritance operates randomly. The seed color of Mendel’s peas can be either green or yellow. Suppose we produce seeds by “crossing’’ two plants, both of which carry the G (green) and Y (yellow) genes. Each parent has probability 1-in-2 of passing each of its genes to a seed, independently of the other parent. A seed will be yellow unless both parents contribute the G gene. Seeds that get two G genes are green.

What is the probability that a seed from this cross will be green? Set up a simulation to answer this question, and estimate the probability from 25 repetitions. (Hint: See page 447.)

III.22. Predicting the winner. There are 14 teams in the Big Ten athletic conference. Here’s one set of personal probabilities for next year’s basketball champion: Michigan State has probability 0.3 of winning. Illinois, Iowa, Minnesota, Nebraska, Northwestern, Penn State, and Rutgers have no chance. That leaves six teams. Indiana, Michigan, Purdue, Ohio State, and Wisconsin also all have the same probability of winning, but that probability is one-half that of Maryland. What probability does each of the 14 teams have?

III.23. Selling cars. Bill sells new cars in a small town for a living. On a weekday afternoon, he will deal with one customer with probability 0.6, two customers with probability 0.3, and three customers with probability 0.1. Each customer has probability 0.2 of buying a car. Customers buy independently of each other.

Describe how you would simulate the number of cars Bill sells in an afternoon. You must first simulate the number of customers, then simulate the buying decisions of one, two, or three customers. Simulate one afternoon to demonstrate your procedure. (Hint: See page 452.)