Three-Way Tables (College Math-1332)

[Jenna]

Hello, my name is Jenna and I am currently taking College Math at Austin Community College.
I have class tomorrow at 8:00am & I am unsure how to solve a problem on my homework.
If anyone can help me at all, it would be greatly appreciated.

[THE PROBLEM]
Use a two-way table or a three-way table to analyze each of the following situations. You may also draw a Venn Diagram to help you visualize each situation.

A survey of 63 business people found that:
30 had desktop computers
22 had laptop computers
39 had a fax machine
15 had a desktop and a laptop
18 had a desktop and a fax machine
14 had a laptop and a fax machine
12 had all three machines

How many of the business people had:
(a) only a laptop?
(b) only a fax machine?
(c) a fax machine and a laptop, but not a desktop?
(d) a fax machine OR a laptop, but not a desktop?
(e) none of the three machines?

 

[arthur ohlsten]

I do not know what a table is, but I will give you the numbers for each term
D= computer
L=laptop
F = fax

Dand L and F=12
D and L and not F=3
L and not D and not F=5
L and F and not D=2
D and F and not not L =6
D and not F and not L =9
F and not D and not L=19

total=56
7 have none

hope this helps
Arthur

 

[mmm4444bot]

I like Venn diagrams.

We use circles to represent overlapping groups.

In this exercise, there are three overlapping groups, desktop owners, laptop owners, and FAX owners.

In the diagram below (double-click to expand), circle D represents desktop owners. Note that four sections comprise circle D (a, d, e, and 12).

Section a represents those who own only a desktop because this section does not overlap either circle L or F.

Section d represents those who own both a desktop and a FAX, but no laptop.

Section e represents those who own both a desktop and a laptop, but no FAX.

12 people own all three.

[attachment=0:14m3ovua]venn.JPG[/attachment:14m3ovua]

First find the values of d, e, and f.

We're told that 15 people own both a desktop and a laptop; the two shaded sections together represent those who own both a desktop and a laptop because that's the overlap between circles D and L.

Therefore, e + 12 = 15, so e must be 3.

Likewise, we're told that d + 12 = 18, so d must be 6.

After we find e, d, and f, we can go on to find a, b, and c.

a + 6 + 3 + 12 = 22

Do you see why?

That's how it goes. Don't forget that there's some people outside of all three circles, too. (I did not label them.) Those are the people who don't own anything.

Let's call them h. You calculate h last.

a + b + c + d + e + f + g + 12 + h = 63