1000 households were surveyed. 275 households own a desktop computer, 455 househ

Question

1000 households were surveyed. 275 households own a desktop computer, 455 households own a DVD player, 405 households own two cars, 145 households own a desktop computer and DVD player, 195 households own a DVD player and two cars, 110 households own two cars and a desktop computer, 265 households do not own a desktop computer, do not own a DVD player, do not own two cars. Find the number of households that own: a desktop computer, DVD player and two cars; only a DVD player; a desktop computer and a DVD player but do not own two cars.

Explanation / Answer

Let us Assume that,
A= Desktop computer
B=DVD Player
C=Two Cars

Given that
n(A)=275
n(B)=455
n(C)=405

n(AUB)=145
n(BUC)=195
n(AUC)=110

n(~(AUBUC))=265
n(A B C) = 1000-265 = 735

n(A B) = n(A) + n(B) n(A B)
145 = 275+455 - n(A B)
n(A B) = 585

n(B C) = n(B) + n(C) n(B C)
195 = 455+405-n(B C)
n(B C) = 665

n(A C) = n(A) + n(C) n(A C)
110 = 275+405-n(A C)
n(A C) = 570

1. n(A B C) = n(A) + n(B) + n(C) n(A B) n(B C) n(A C) + n(A B C)
= 275+455+405-585-665-570+735
   = 50

3. n(A B C') = n(A B)-n(A B C)
= 145-50
       = 95

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.