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In a survey, 676 adults were asked what television programs they had recently watched. The following information was obtained: 228 adults watched neither the Big Game nor the New Movie, and 287 watched the New Movie. If 181 of those who watched the New Movie did not watch the Big Game, how many of the surveyed adults watched the following?(a) both programs(b) at least one program(c) the Big Game(d) the Big Game but not the New Movie

Question

In a survey, 676 adults were asked what television programs they had recently watched. The following information was obtained: 228 adults watched neither the Big Game nor the New Movie, and 287 watched the New Movie. If 181 of those who watched the New Movie did not watch the Big Game, how many of the surveyed adults watched the following?(a) both programs(b) at least one program(c) the Big Game(d) the Big Game but not the New Movie

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Solution

(a) To find the number of adults who watched both programs, we first need to find out how many adults watched the New Movie and the Big Game. We know that 287 adults watched the New Movie, and out of those, 181 did not watch the Big Game. So, the number of adults who watched both programs is 287 (total who watched the New Movie) - 181 (those who watched the New Movie but not the Big Game) = 106.

(b) To find the number of adults who watched at least one program, we subtract the number of adults who watched neither program from the total number of adults surveyed. So, 676 (total adults) - 228 (those who watched neither) = 448 adults watched at least one program.

(c) To find the number of adults who watched the Big Game, we add the number of adults who watched both programs to the number of adults who watched the Big Game but not the New Movie. We already know that 106 adults watched both programs. We can find the number of adults who watched the Big Game but not the New Movie by subtracting the number of adults who watched both programs and the number of adults who watched neither program from the total number of adults. So, 676 (total adults) - 106 (both programs) - 228 (neither program) = 342 adults watched the Big Game.

(d) To find the number of adults who watched the Big Game but not the New Movie, we subtract the number of adults who watched both programs from the total number of adults who watched the Big Game. So, 342 (total who watched the Big Game) - 106 (both programs) = 236 adults watched the Big Game but not the New Movie.

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