SOLUTION: A survey of a group's sports viewing habits over the last year revealed the following information: I. 28% watched soccer ii. 29% watched basketball iii. 19% watched tennis i

Question 1063420: A survey of a group's sports viewing habits over the last year revealed the following information:
I. 28% watched soccer
ii. 29% watched basketball
iii. 19% watched tennis
iv. 14% watched soccer and basketball
v. 12% watched basketball and tennis
vi. 10%watched soccer and tennis
vii. 8% watched all three sports
What percent of the group watched none of the three sports last year?
Pleaseeee explain. I really don't understand. Thankyou so much.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
To solve this, you have to understand Venn diagrams,
and this particular Venn diagram.
---------------------------------
When they say 28% watched soccer, some of that 28%
also watched tennis and basketball.
If you add up , they all watched
more than one sport, and there were some who watched all three
sports. Also, some watched none of these sports.
---------------------------------------------
A Venn diagram is made up of 3 interlocking circles with a
region in the middle where all 3 circles have a common area.
The circles are the 28%, 29%, and 19% given.
-----------------------------------------------------
The key to using the Venn diagram is to realize there are
7 separate areas to consider and focus on. The 7 areas are:
(1) watched ONLY soccer
(2) watched ONLY basketball
(3) watched ONLY tennis
(4) watched ONLY soccer and basketball
(5) watched ONLY soccer and tennis
(6) watched ONLY tennis and basketball
(7) watched all 3 sports
--------------------------------------
Draw the 3 interlocking circles, then label the 7 sepatate
areas with symbols, so you are keeping them straight in your mind.
---------------------------------------
**IMPORTANT**
Another key to to the solution is to start with the area in the
middle which is (7) watched all 3 sports = 8%
------------------------------------------
Subtract area (7) from watched soccer and basketball = 14%
giving you
(4) 6% watched ONLY soccer and basketball
So you have 1 of the 7 needed areas. ( plus area (7) )
-----------------------------------------
Subtract area (7) from watched soccer and tennis = 10%
giving you
(5) 2% watched ONLY soccer and tennis
Now you have 2 of the 7 needed areas
------------------------------------------
Subtract area (7) from watched basketball and tennis - 12%
giving you
(6) 4% watched ONLY tennis and basketball
You have 3 of the 7 needed areas ( plus area (7) )
--------------------------------------------
The 3 areas remaining are:
(1) watched ONLY soccer
(2) watched ONLY basketball
(3) watched ONLY tennis
------------------------------
By looking at the Venn diagram, you should be able to see:
(1) watched ONLY soccer = 12%
(2) watched ONLY basketball = 11%
(3) watched ONLY tennis = 5%
--------------------------------------------------------
Now that these 7 areas are determined, you can solve ANY
problem. The question is: what % watched NONE of the 3 sports.
Add up the 7 areas:

So 48% watched at least 1, maybe more, of these sports. That
means 52% watch NONE of these sports.
---------------------------------------------------------
Keep in mind I could have mistakes and gotten some ( or maybe all )
of this wrong, but this is DEFINITELY the right approach, and that
is all you care about. It's a head-banger for sure, but you just have to
keep at it and don't give up. Understanding is the key.
Hope this helps

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