A number of yugo owners were surveyed regarding their favourite activities. 57 enjoy walking, 65 enjoy waiting for tow trucks, 60 enjoy hitchhiking, 20 enjoy waiting for tow trucks and enjoy hitchhiking and enjoy walking. 22 enjoy hitchhiking and enjoy walking. 12 don't enjoy waiting for tow trucks and don't enjoy hitchhiking and don't enjoy walking. 23 enjoy walking but don't enjoy hitchhiking and don't enjoy waiting for tow trucks, 38 enjoy waiting for tow trucks and enjoy hitchhiking.
A) How many were surveyed?
B) How many enjoy atleast two of these activities?
Answers
Given : details of surveys regarding their favourite activities.
To find : A) How many were surveyed?
B) How many enjoy atleast two of these activities?
Solution:
W = 57
T = 65
H = 60
W ∩ T ∩ H = 20
H ∩ W = 22
None = 12
T ∩ H = 38
Only walking = 23
only walking = W - H ∩ W - T ∩ W + W ∩ T ∩ H
23 = 57 - 22 - T ∩ W + 20
=> T ∩ W = 32
Total = W + T + H - H ∩ W - T ∩ H - T ∩ W + W ∩ T ∩ H + None
Total = 57 + 65 + 60 - 22 - 38 - 32 + 20 + 12
=> Total = 122
122 were Surveyed
atleast two of these activities
H ∩ W + T ∩ H + T ∩ W - 2 * W ∩ T ∩ H
= 22 + 38 + 32 - 2 * 20
= 52
52 enjoy atleast two of these activities
122 were Surveyed
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