6. A department store surveyed 428 shoppers, and the following information was o

Question

6. A department store surveyed 428 shoppers, and the following information was obtained: 214 made a purchase, and 299 were satisfied with the service they received. If 52 of those who made purchase were not satisfied with the service, how many shoppers did the following?      (two events problem purchase, P satisfied, S)                                                                                      15 points

a. made a purchase and were satisfied with the service

b. made a purchase or were satisfied with the service

c. were satisfied with the service but did not make a purchase

d. were not satisfied and did not make a purchase

Explanation / Answer

Let A denote a shopper who made a purchase and B denote a shopper who was satisfied. Let U denote all shoppers.

Given n(U) = 428 n(A) = 214 n(B) = 299 n(A Bc) = 52

a. n(A B) = n(A) - n(A Bc)

= 214 - 52

= 162

b. n(A U B) = n(A) + n(B) - n(A B)

= 214 + 299 - 162

= 351

c. P(Ac B) = P(B) - P(A B)

= 299 - 162

= 137

d. P(Ac Bc)

= P(A U B)c according to De-Morgan's law

= P(U) - P(A U B)

= 428 - 351

= 77

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