Contingency table
4.3 Consider the following contingency table:
B B.
A 10 20
A. 20 40
What is the probability of event
a. A?
b.
c. A and B?
d. A or B?
4.9 Referring to the contingency table in Problem 4.8, if a large online retailer is selected at random, what is the probability that
a. you needed three or more clicks to be removed from an
email list?
b. you needed three or more clicks to be removed from an
email list in 2009?
c. you needed three or more clicks to be removed from an
email list or were a large online retailer surveyed in 2009?
d. Explain the difference in the results in (b) and (c).
NEED THREE OR MORE CLICKS TO BE REMOVED
YEAR Yes NO
2009 39 61
2008 7 93
4.15 Each year, ratings are compiled concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether a car needs warranty-related repair (yes or no) and the country in which the company manufacturing a car is based (United States or not United States). Based on the data collected, the probability that the new car needs a warranty repair is 0.04, the probability that the car was manufactured by a U.S.-based company is 0.60, and the probability that the new car needs a warranty repair and was manufactured by a U.S.-based company is 0.025. Construct a contingency table to evaluate the probabilities of a warranty-related repair. What is the probability that a new car selected at random
a. needs a warranty repair?
b. needs a warranty repair and was manufactured by a U.S.-based company?
c. needs a warranty repair or was manufactured by a U.S.- based company?
d. needs a warranty repair or was not manufactured by a U.S.-based company?
4.19IfP(A) = 0.7, P(B) = 0.6, and A and B are independent,
findP(A and B).
4.23 What is the preferred way for people to order fast food? A survey was conducted in 2009, but the sample sizes were not reported. Suppose the results, based on a sample of 100 males and 100 females, were as follows:
GENDER
DINING PREFERENCE Male Female Total
Dine inside 21 12 33
Order inside to go 19 10 29
Order at the
drive-through 60 78 138
Total 100 100 200
a. Given that a respondent is a male, what is the probability that he prefers to order at the drive-through?
b. Given that a respondent is a female, what is the probability that she prefers to order at the drive-through?
c. Is dining preference independent of gender?
Explain.
4.26 Each year, ratings are compiled concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether a car needs warranty-related repair (yes or no) and the country in which the company manufacturing a car is
based (United States or not United States). Based on the data collected, the probability that the new car needs a warranty repair is 0.04, the probability that the car is manufactured
by a U.S.-based company is 0.60, and the probability that the new car needs a warranty repair and was manufactured by a U.S.-based company is 0.025.
a. Suppose you know that a company based in the United States manufactured a particular car. What is the probability that the car needs warranty repair?
b. Suppose you know that a company based in the United States did not manufacture a particular car. What is the probability that the car needs warranty repair?
c. Are need for warranty repair and location of the company manufacturing the car independent?
4.61 The owner of a restaurant serving Continental-styleentrees was interested in studying ordering patterns of patrons for the Friday-to-Sunday weekend time period.Records were maintained that indicated the demand for dessert during the same time period. The owner decided to study two other variables, along with whether a dessert was ordered: the gender of the individual and whether a beef
entree was ordered. The results are as follows:
GENDER
DESSERT ORDERED Male Female Total
Yes 96 40 136
No 224 240 464
Total 320 280 600
BEEF ENTRÉE
DESSERT ORDERED Yes No Total
Yes 71 65 136
No 116 348 464
Total 187 413 600
A waiter approaches a table to take an order for dessert. What is the probability that the first customer to order at the table
a. orders a dessert?
b. orders a dessert or has ordered a beef entree?
c. is a female and does not order a dessert?
d. is a female or does not order a dessert?
e. Suppose the first person from whom the waiter takes the dessert order is a female. What is the probability that she does not order dessert?
f. Are gender and ordering dessert independent?
g. Is ordering a beef entree independent of whether the person orders dessert?
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