An insurance company is surveying travellers, to learn how much of their summer travel is taken
with an airplane, a train or a car. The following data is known; make a complete Venn Diagram
with all the data. The number of people who flew was 1307. The number of people who both flew
and used a train was 602. The people who used all three were 398 in number. Those who flew but
didn't drive came to a total of 599. Those who drove but did not use a train were 1097. There
were 610 people who used both trains and cars. The number of people who used either a car or a
train or both was 2050. Lastly, 421 people used none of these. Find
Answers
Given : An insurance company is surveying travellers, to learn how much of their summer travel is taken with an airplane, a train or a car
To Find : Draw venn Diagram
Solution:
Flew F = 1307
Train T
Car C
flew and used a train F ∩ T = 602
used all three F ∩ T ∩ C = 398
flew but didn't drive = F - F ∩ C = 599 => 1307 - F ∩ C = 599
=> F ∩ C = 708
both trains and cars. C ∩ T = 610
drove but did not use a train = C - C ∩ T = 1097 => C - 610 = 1097
=> C = 1707
either a car or a train or both C + T - C ∩ T = 2050
=> 1707 + T - 610 = 2050
=> T = 953
Total = F + C + T - F ∩ T - C ∩ T - F ∩ C + F ∩ T ∩ C + None
= 1307 + 1707 + 953 - 602 - 610 - 708 + 398 + 421
= 2866
Total = 2866
Venn diagram attached
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