Question

a magazine surveyed subscribers, asking which of the following reality shows they watched on a regular basis: survivor, the voice, america’s got talent. the results showed that 358 watched survivor, 295 watched the voice, 285 watched america’s got talent, 194 watched survivor and the voice, 202 watched survivor and america’s got talent, 139 watched the voice and america’s got talent, 68 watched survivor, the voice, and america’s got talent, and 27 watched none of these shows. complete parts a) through e) below.
a) how many subscribers were surveyed?
498 (simplify your answer.)
b) of the subscribers surveyed, how many watched survivor and america’s got talent, but not the voice?
134 (simplify your answer.)
c) of the subscribers surveyed, how many watched the voice, but neither survivor nor america’s got talent?
30 (simplify your answer.)
d) of the subscribers surveyed, how many watched exactly two of these shows?
331 (simplify your answer.)
e) of the subscribers surveyed, how many watched at least one of these shows?
□ (simplify your answer.)

Explanation:

Step1: Recall the total surveyed and those who watched none

We know the total number of subscribers surveyed is 498 (from part a), and 27 watched none.

Step2: Calculate those who watched at least one

To find the number who watched at least one, we subtract the number who watched none from the total surveyed. So we use the formula: $ \text{At least one} = \text{Total surveyed} - \text{Watched none} $
Substituting the values: $ 498 - 27 = 471 $

Answer:

471