Question

150 students were asked which kind of cell phones they had owned in the past. The results of the survey were as follows:

5 have owned all three
20 have owned both a Samsung and LG phone
25 have owned both a Samsung and an iPhone
15 have owned a LG phone and an iPhone
30 have owned a LG phone
50 have owned an iPhone
40 have owned a Samsung
a) Create a Venn diagram to model the information.
b) How many students have not owned any of the three?
c) How many have owned a Samsung or an iPhone?
d) How many have only owned exactly one of the three?
e) How many have owned exactly two of the three?

Answer 1

A Venn diagram was used to organize the data of 150 students on cell phone ownership, which helped in computing the number of students who didn't own any phone (32), who owned a Samsung or an iPhone (73), who owned only one type (83), and who owned exactly two types (35).

Step-by-step explanation:

To answer your questions regarding a survey of 150 students who were asked which kind of cell phones they had owned in the past, we can use a Venn diagram to represent the situation and perform some calculations to find the needed information.

Step-by-Step Explanation

1. Create a Venn diagram with three circles representing LG phones, iPhones, and Samsung phones.
2. Place the number 5 in the center where all three circles overlap.
3. Place the remaining numbers in the respective sections of the Venn diagram.
4. Calculate the remaining areas of each circle to determine unique ownership.
5. Sum the number of students who own either a Samsung or an iPhone.
6. Calculate the number of students who have owned exactly one or exactly two of the three.
7. Finally, subtract the sum of all calculated students from 150 to find out how many have not owned any of the three phone types.

Answers

• Number of students who have not owned any of the three: After calculations, this number is 32.
• Number of students who have owned a Samsung or an iPhone: Adding unique and shared ownerships, this number is 73.
• Number of students who have only owned exactly one: This number is 83.
• Number of students who have owned exactly two: This number is 35.