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Answer :
40 adults did not travel by any of the given modes of transportation.
To determine the number of adults who did not travel by any of the given modes of transportation, we need to calculate the complement of the set of adults who traveled by at least one of the modes.
Let's break down the given information using a Venn diagram to visualize the different groups:
1. Let A represent the set of adults who traveled by plane.
2. Let B represent the set of adults who traveled by train.
3. Let C represent the set of adults who traveled by bus.
Based on the information provided:
- We know that 65 adults traveled by plane but not by train (A - (A ∩ B)).
- Similarly, 65 adults traveled by train but not by plane (B - (A ∩ B)).
- 35 adults traveled by bus but not by plane or train (C - (A ∪ B)).
- 90 adults traveled by both bus and plane (A ∩ C).
- 45 adults traveled by all three modes (A ∩ B ∩ C).
- Lastly, 195 adults traveled by plane or train (A ∪ B).
To find the number of adults who did not travel by any of these modes, we need to calculate the complement of (A ∪ B ∪ C) within the total population of 250 adults.
Let's calculate:
Total adults who traveled by at least one mode = (A ∪ B ∪ C) = (A + B + C) - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C)
= 65 + 65 + 35 + 90 - 45
= 210
Therefore, the number of adults who did not travel by any of these modes is:
Total population - Total adults who traveled by at least one mode = 250 - 210 = 40.
Hence, 40 adults did not travel by any of the given modes of transportation.
Learn more about modes of transportation here:-
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