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Answer:
The number of households that had at least one of the three devices is 70.
Step-by-step explanation:
The data provided is as follows:
n (C) = 40
n (PC) = 60
n (T) = 50
n (C ∩ PC) = 25
n (PC ∩ T) = 30
n (C ∩ T) = 35
n (C ∩ PC ∩ T) = 10
Compute the number of households that had at least one of the three devices as follows:
[tex]n (C \cup PC \cup T) = n (C) + n (PC) + n (T) - n (C \cap PC) - n (PC \cap T) - n (C \cap T) \\ \ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ + n (C \cap PC \cap T)[/tex]
[tex]=40+60+50-25-30-35+10\\=70[/tex]
Thus, the number of households that had at least one of the three devices is 70.
A survey is a research method used for collecting data and then analyse.
The number of households that had at least one of the three devices is 70.
According to question,
Since, 40 had a cell phone, [tex]n (C) = 40[/tex]
60 had a personal computer [tex]n (PC) = 60[/tex]
50 had a television [tex]n (T) = 50[/tex]
25 had a cell phone and a personal computer n (C ∩ PC) = 25
30 had a personal computer and a television ,n(PC ∩ T) = 30
35 had a cell phone and a television , n (C ∩ T) = 35
10 had all three ,n (C ∩ PC ∩ T) = 10
We know that,
[tex]n(C\cup PC\cup T)=n(C)+n(PC)+n(T)-n(C\cap PC)-n(PC\cap T)-n(C\cap T)+n(C\cap PC\cap T)[/tex]
[tex]n(C\cup PC\cup T)=40+60+50-25-30-35+10=70[/tex]
Therefore, 70 households that had at least one of the three devices.
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