Answer:
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
<u>Formula:</u>
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
<u>Formula:</u>
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, <em>n(B - A)</em>
<u>Formula:</u>
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.