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Some customers of a retail chain have a store credit card that earns them bonus gifts when they make purchases at the chain. Currently, 28 customers are shopping in a store in this chain. Of these, half already have a store credit card. If employees offer store credit cards to 7 of these, what is the probability that all of those chosen already have a card? Complete parts (a) through (e) below.

Some customers of a retail chain have a store credit card that earns them bonus gifts when they make purchases at the chain. Currently, 28 customers are shopping in a store in this chain. Of these, half already have a store credit card. If employees offer store credit cards to 7 of these, what is the probability that all of those chosen already have a card? Complete parts (a) through (e) below.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Some customers of a retail chain have a store credit card that earns them bonus gifts when they make purchases at the chain. Currently, 28 customers are shopping in a store in this chain. Of these, half already have a store credit card. If employees offer store credit cards to 7 of these, what is the probability that all of those chosen already have a card? Complete parts (a) through (e) below. (a) Explain why it would not be appropriate to use a binomial model for the number of customers who already have a store credit card, among the 7 customers who were chosen. A. The number who already have a card in the 7 customers who were offered a store credit card is not a random variable. B. There are not two possible outcomes for each trial involved in randomly selecting the 7 customers who were offered a store credit card. C. The subset of the 7 customers who were offered a store credit card is too large and violates the 10% condition. D. The number who already have a card in the 7 customers who were offered a store credit card meets all of the conditions for using a binomial model. (b) A family of 7 is shopping in the store. Noting that nCx gives the number of ways of picking a subset of x items out of n, what is the probability that the 7 randomly selected shoppers are in this family? The probability that the 7 randomly selected shoppers are in this family is .071429 (Round to seven decimal places as needed.)
Transcribed Image Text:Some customers of a retail chain have a store credit card that earns them bonus gifts when they make purchases at the chain. Currently, 28 customers are shopping in a store in this chain. Of these, half already have a store credit card. If employees offer store credit cards to 7 of these, what is the probability that all of those chosen already have a card? Complete parts (a) through (e) below. (a) Explain why it would not be appropriate to use a binomial model for the number of customers who already have a store credit card, among the 7 customers who were chosen. A. The number who already have a card in the 7 customers who were offered a store credit card is not a random variable. B. There are not two possible outcomes for each trial involved in randomly selecting the 7 customers who were offered a store credit card. C. The subset of the 7 customers who were offered a store credit card is too large and violates the 10% condition. D. The number who already have a card in the 7 customers who were offered a store credit card meets all of the conditions for using a binomial model. (b) A family of 7 is shopping in the store. Noting that nCx gives the number of ways of picking a subset of x items out of n, what is the probability that the 7 randomly selected shoppers are in this family? The probability that the 7 randomly selected shoppers are in this family is .071429 (Round to seven decimal places as needed.)
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