Chapter 12Section 4

Bell Ringer7. A public opinion poll in Ohio wants to determine whether registered voters in the state approve of a measure to ban smoking in all public areas. The researchers select a simple random sample of 50 registered voters from each county in the state and ask whether they approve or disapprove of the measure. This is an example of a. a systematic county sample.b. a stratified sample.c. a multistage sample.d. a simple random sample.

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Section 4

In general, if all outcomes in a sample space are equally likely, we find the probability of any event by

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12.8 Who Takes the GMAT?In many settings, the “rules of probability” are just basic facts about percents. The Graduate Management Admission Test (GMAT) website provides the following information about the geographic regions of those who took the test in 2012–13: 2.3% were from Africa; 0.4% were from Australia and the Pacific Islands; 2.7% were from Canada; 11.5% were from Central and South Asia; 29.1% were from East and Southeast Asia; 2.1% were from Eastern Europe; 2.8% were from Mexico, the Caribbean, and Latin America; 3.6% were from the Middle East; 38.0% were from the United States; and 7.4% were from Western Europe.3

(a)What percent of those who took the test in 2012–13 were from North America (either Canada, the United States, Mexico, the Caribbean, or Latin America)? Which rule of probability did you use to find the answer?

(b)What percent of those who took the test in 2012–13 were from some other region than the United States? Which rule of probability did you use to find the answer?

12.9 Overweight? Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American adult aged 20 years and over at random. Define two events:

A = the person chosen is obeseB = the person chosen is overweight, but not obese

According to the National Center for Health Statistics, P(A) = 0.36 and P(B) = 0.33.

(a)Explain why events A and B are disjoint.

(b)Say in plain language what the event “A or B” is. What is P(A or B)?

(c)If C is the event that the person chosen has normal weight or less, what is P(C)?

12.10 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 province of Quebec:

(a)What is the probability that a Canadian’s mother tongue is either English or French?

(b)What probability should replace “?” in the distribution?

(c)What is the probability that a Canadian’s mother tongue is not English?

12.11 Are They Disjoint? Which of the following pairs of events, A and B, are disjoint? Explain your answers.

(a)A person is selected at random. A is the event “sex of the person selected is male” and B is the event “sex of the person selected is female.”

(b)A person is selected at random. A is the event “the person selected earns more than $100,000 per year” and B is the event “the person selected earns more than $250,000 per year.”

(c)A pair of dice are tossed. A is the event “one of the dice is a 3” and B is the event “the sum of the two dice is 3.”