Question

1) A case of 24 cans contains 1 can that is contaminated. Three cans are to be chosen randomly for testing. How many different sets of 3 cans could be selected?

2) A state’s license plate has 6 positions, each of which has 37 possibilities (letter, integer, or blank). If someone requests a license plate with the first three positions to be BMW how many different license plates would satisfy this request?

3) The U.S. Census Bureau reports that 35% of adults attend a sporting event each year. What are the odds a randomly selected adult in the U.S. attended a sporting event last year?

4) You have to go to 5 different buildings on campus to turn in assignments. How many different orders could you follow when visiting the 5 buildings?

5) A casino in Las Vegas showed that the odds of the Minnesota Twins beating the Detroit Tigers in a baseball game as 4:7. What is the probability the Minnesota Twins will win the game? 6) John and Jane are married. The probability that John watches a certain television show is 0.4. The probability that Jane watches the show is 0.5. The probability that John watches the show, given that Jane does is 0.70. a) Find the probability that both John and Jane watch the show. b) Do John and Jane watch the show independently of each other? Justify your answer. c) Find the probability that either John or Jane watches the show.

7) The U.S. Census Bureau reports that 90.4% of adults aged 25 and over who are employed have graduated from high school and 34.0% of adults aged 25 and over who are employed have graduated from college. Assume that an adult aged 25 and over who has graduated from college also graduated from high school. a) What is the probability an adult aged 25 and over who is employed did not graduate from high school. b) What is the probability an adult aged 25 and over who is employed that graduated from high school also graduated from college? c) What is the probability an adult aged 25 and over who is employed that graduated from high school did not graduate from college? d) Are the events H (Employed adult aged 25 and over who graduated from high school) and C (Employed adult aged 25 and over who graduated from college) independent?

8) A survey of 400 undergraduate college students was conducted to study their views on government and the economy. The Survey worksheet of the HW1 data workbook on Moodle contains each student’s class standing and response to question 7 - which read “The job market will be better when I graduate than when I started college”. a) Construct a contingency table that has one row for each class standing and one column for each response. b) What is the probability a survey respondent is in their sophomore year? What type of probability is this? c) What is the probability a survey respondent Strongly Agrees with Question 7? What type of probability is this? d) What is the probability a sophomore survey respondent Strongly Agrees with Question 7? What type of probability is this? e) What is the probability a survey respondent is a Freshman who Disagrees with question 7? What type of probability is this? f) Are class standing and response to question 7 independent? Why?

Answer 1

1) There are 2 possible cases here

(a) Contaminated can is selected: This means 1 contaminated can is selected and 2 out of the remaining 23 cans is selected in 23C2 ways. Hence total number of cases here is 23C2*1C1= 23C2.

(b) Contaminated can is not selected: This means that we select the 3 cans from the 23 non-contaminated cans. Hence total number of cases here is 23C3.

Hence total number of cases = 23C2+ 23C3= 253+1771= 2024.

2) Here if we consider 6 positions like _ _ _ _ _ _ and since first three are BMW, so we get BMW_ _ _. 4th position can be any of the 37 possibilities.

5th position can be any of the 37 possibilities.

6th position can be any of the 37 possibilities.

Hence last 3 positions can be filled in 37*37*37 possibilitites = 50653 number plates. (even if any 1 component varies, it would be a new plate)

3) Let p be the % of adults attend a sporting event each year. Given p=35% = 0.35. The odds of a randomly selected adult attending a sporting event last year = p/(1-p) = 0.35/0.65 = .5385 54%

4) If we have to visit 5 different buildings on campus, then

We can first visit 5 possible buildings

We can next visit 4 possible buildings (excluding the one we have visited)

We can next visit 3 possible buildings (excluding the two we have visited)

We can next visit 2 possible buildings (excluding the three we have visited)

We can next visit the only building left.

Hence number of orders = 5*4*3*2*1 = 120