A survey of 70 college students showed the following data: 42 had a ca

vousetmoiec

vousetmoiec

Answered question

2021-12-04

A survey of 70 college students showed the following data: 42 had a car; 50 had a TV; 30 had a bicycle; 17 had a car and a bicycle; 35 had a car and a TV; 25 had a TV and a bicycle; 15 had all three. How many students had none of the three items?

Answer & Explanation

Alfonso Miller

Alfonso Miller

Beginner2021-12-05Added 20 answers

Step 1 
According to a survey of 70 college students, 42 had a car, 50 had a TV, 30 had a bicycle, 17 owned both a car and a bicycle, 35 owned both a car and a television, 
Step 2 
That is, n(C)=43,n(T)=50,n(B)=30,n(C  and  B)=17,n(C  and  T)=35,n(T  and  B)=25  and  n(C  and  T  and  B)=15
Total students is n=70
Thus, the number of students, who had either car or TV or bicycle is, 
n(C  or  T  or  B)=n(C)+n(T)+n(B)n(C  and  B)n(C  and  T)n(T  and  B)+n(C  and  T  and  B)=43+50+30173525+15=61
Thus, the number of students, had none of the three items is nn(C  or  R  or  B)=7061=9.

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