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Burka [1]
3 years ago
14

A department store surveyed 428 shoppers, and the following information was obtained: 216 shoppers made a purchase, and 294 were

satisfied with the service they received. If 47 of those who made a purchase were not satisfied with the service, how many shoppers did the following?a. made a purchase and were satisfied with the service
b. made a purchase or were satisfied with the serice
c. were satisfied with the service but did not mak a purchase
d. were not satisfied and did not make a purchase

Mathematics
1 answer:
Maurinko [17]3 years ago
6 0

Answer:

(a) 169

(b) 341

(c) 125

(d) 87

Step-by-step explanation:

Consider the Venn diagram below.

The total number of shoppers surveyed is, <em>N</em> = 428.

Number of shoppers who made a purchase, <em>n</em> (P) = 216

Number of shoppers who were satisfied with the service they received,

<em>n</em> (S) = 294

Number of shoppers who made a purchase but were not satisfied with the service, n(S^{c}\cap P) = 47

(a)

The number of shoppers who made a purchase and were satisfied with the service = <em>n</em> (S ∩ P)

             n(S\cap P)=n(P)-n(S^{c}\cap P)\\=216-47\\=169

(b)

The numbers of shoppers who made a purchase or were satisfied with the service = <em>n</em> (P ∪ S)

               n(P\cup S)=n(P)+n(S)-n(P\cap S)\\=n(P)+n(S)-n(S\cap P)\\=216+294-169\\=341

(c)

The numbers of shoppers who were satisfied with the service but did not make a purchase = n(S\cap P^{c})

n (S\cap P^{c} ) = n (S) - n (S \cap P)\\=294-169\\=125

(d)

The number of shoppers who were not satisfied and did not make a purchase  = n(S^{c}\cap P^{c})

n(S^{c}\cap P^{c})=N-n(S\cup P)\\=N-n(P\cup S)\\=428-341\\=87

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