Of 10,000 students at a college, 2,500 have a Mastercard ( M), 4,000 have a VISA ( V), and 1,000 have both.
a Find the probability that a randomly selected student
( 1) Has a Mastercard.
( 2) Has a VISA.
( 3) Has both credit cards.
b Construct and fill in a contingency table summarizing the credit card data. Employ the following pairs of events: M and M , V and V .
c Use the contingency table to find the probability that a randomly selected student
( 1) Has a Mastercard or a VISA.
( 2) Has neither credit card.
( 3) Has exactly one of the two credit cards.
4.14 page 169
In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle present the results of a concept study for a new wine cooler. Three hundred consumers between 21 and 49 years old were randomly selected. After sampling the new beverage, each was asked to rate the appeal of the phrase
Not sweet like wine coolers, not filling like beer, and more refreshing than wine or mixed drinks as it relates to the new wine cooler. The rating was made on a scale from 1 to 5, with 5 representing “ extremely appealing” and with 1 representing “ not at all appealing.” The results obtained are given in Table 4.4. Estimate the probability that a randomly selected 21- to 49- year- old consumer
a Would give the phrase a rating of 5.
b Would give the phrase a rating of 3 or higher.
c Is in the 21– 24 age group; the 25– 34 age group; the 35– 49 age group.
d Is a male who gives the phrase a rating of 4. e Is a 35- to 49- year- old who gives the phrase a rating of 1.
4.19 page 176
Recall from Exercise 4.13 ( page 169) that each month a brokerage house studies various compa-nies and rates each company’s stock as being either “ low risk” or “ moderate to high risk.” In a recent report, the brokerage house summarized its findings about 15 aerospace companies and 25 food retailers in the following table:
Company Type Low Risk Moderate to High Risk
Aerospace company 6 low risk 9 moderate to high risk
Food retailer 15 low risk 10 moderate to high risk
A department store is considering a new credit policy to try to reduce the number of customers de-faulting on payments. A suggestion is made to discontinue credit to any customer who has been one week or more late with his/ her payment at least twice. Past records show 95 percent of defaults were late at least twice. Also, 3 percent of all customers default, and 30 percent of those who have not defaulted have had at least two late payments.
a Find the probability that a customer with at least two late payments will default.
b Based on part a, should the policy be adopted? Explain.