Final answer:
Using the principle of inclusion-exclusion for three sets, it was calculated that 9 people read only the Tribune, and 65 people read none of the papers from a survey of 214 people.
Step-by-step explanation:
To determine the number of people who read the Tribune and those who read none of the papers, we can use the principle of inclusion-exclusion for three sets. Let's denote the number of people who read the Guardian, Sketch, and Tribune as G, S, and T, respectively. The problem states that:
- G = 100
- S = 90
- T = 85
- G ∩ S (both Guardian and Sketch) = 50
- G ∩ T (both Guardian and Tribune) = 45
- S ∩ T (both Sketch and Tribune) = 66
- G ∩ S ∩ T (all three papers) = 35
To find how many read the Tribune (question 1), we take the total number of Tribune readers (85) and subtract those who read both Tribune and another paper to avoid double counting, then add back in those who read all three because they've been subtracted twice:
T only = T - (G ∩ T) - (S ∩ T) + (G ∩ S ∩ T)
T only = 85 - 45 - 66 + 35 = 9
To find how many read none of the papers, we take the total number surveyed (214) and subtract those who read at least one paper:
Total Surveyed = 214
Total reading at least one paper = G + S + T - (G ∩ S) - (G ∩ T) - (S ∩ T) + (G ∩ S ∩ T)
Total reading at least one paper = 100 + 90 + 85 - 50 - 45 - 66 + 35
Total reading at least one paper = 149
Therefore, the number of people who read none of the papers is:
None = Total Surveyed - Total reading at least one paper
None = 214 - 149 = 65