# Probability and Permutation Questions

3. How many permutations of three items can be selected from a group of six? Use the letters A,B,C,D,E and F to identify the items, and list each of the permutations of items B,D and F

11. The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the United States are using seat belts(Associated Press,August 25,2003). Sample data consistent with the NHTSA survey are as follows

Driver using seat belt?

Region Yes No

Northeast 148 52

Midwest 162 54

South 296 74

West 252 48

Total 858 228

a. For the United States, what is the probability that a druver is using a seat belt?

b. The seat belt usage probability fir a U.S driver a year earlier was .75. NHTSA chief Dr.Jeffrey Runge had hoped for a .78 probability in 2003. Would he have been pleased with the 2003 survey results?

c. What is the probability of seat belt usage by region of the country? What region has the highest seat belt usage?

d. What proportion of the drivers in the sample came from each region of the country?

e. Assuming the total number of drivers in each region is the same, do you see any reason why the probability estimate in part (a) might be too high? Explain.

23.Suppose that we have a sample space S={E1,E2,E3,E4,E5,E6,E7}, where E1,E2,...,E7 denote the sample points. The following probability assignments apply : P(E1)=.05,P(E2)=.20, P(E3)=.20, P(E4)=.25, P(E5)=.1, P(E6)=.10, P(E7)=.05 . Let

A={E1,E4,E6}

B={E2,E4.E7}

C={E2,E3,E5,E7}

a.Find P(A), P(B), and P(C)

b.Find A υ B and P(A U B)

c. Are events A and C mutually exclusive?

d.Find Bc and P(Bc)

27. A 2001 preseason NCAA football poll asked respondents to answer the question, "Will the Big Ten or the Pac-lO have a team in this year's national championship game, the Rose Bowl?" Of the 13,429 respondents, 2961 said the Big Ten would,4494 said the Pac-10 would, and 6823 said neither the Big Ten nor the Pac-10 would have a team in Rose Bowl (http://www.yahoo.com,August 30,2001)

a. What is the probability that a respondent said neither the Big Ten nor the Pac-10 will have a team in the Rose Bowl?

b. What is the probability that a respondent said either the Big Ten or the Pac-10 will have a team in the Rose Bowl?

c. Find the probability that a respondent said both the Big Ten and the Pac-10 would have a team in the Rose Bowl.

#### Solution Summary

Detailed solutions have been provided for all the questions.