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mia2286
19.06.2020 •
Mathematics
In a survey, 672 adults were asked what television programs they had recently watched. The following information was obtained: 226 adults watched neither the Big Game nor the New Movie, and 287 watched the New Movie. If 183 of those who watched the New Movie did not watch the Big Game, how many of the surveyed adults watched the following?
a. the Big Game.
b. the Big Game but not the New Movie.
c. at least one program.
d. both programs.
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Ответ:
a. the Big Game = 263
b. the Big Game but not the New Movie = 159
c. at least one program = 446
d. both programs = 104.
Step-by-step explanation:
Given that:
Total adults asked about TV programs, n(U) = 672
Total adults who watch New Movie, n(A) = 287
Let n(B) be the number of adults who watch Big Game.
Total adults who watch New Movie but not Big Game, n(A-B) = 183
As per formula:
n(A-B) = n(A) - n(A
B)
Where n(A
B) is the number of adults who watch New Movie and Big Game both.
n(A
B) = n(A) - n(A-B)
n(A
B) = 287 - 183 = 104
Formula:
n(U) = n(A
B) + n(A
B)'
n(A
B) is the number of adults who watch at least one program.
n(A
B)' is the number of adults who do not watch any program.
Given that n(A
B)' = 226
Putting values in the above formula:
672 = n(A
B) + 226
n(A
B) = 672 - 226 = 446
Formula:
n(A
B) = n(A) + n(B) - n(A
B)
446 = 287 + n(B) - 104
n(B) = 446 + 104 - 287
n(B) = 263
The number of adults who watch the Big Game but not the New Movie, n(B - A)
Formula:
n(B - A) = n(B) - n(A
B)
n(B - A) = 263 - 104 = 159
So, the number of surveyed adults who watch:
a. the Big Game, n(A) = 263
b. the Big Game but not the New Movie, n(B - A) = 159
c. at least one program, n(A
B) = 446
d. both programs, n(A
B) = 104.
Ответ: