Question 757145: In a survey of college students, it was found that:
356 owned an iPod
293 owned a laptop
285 owned a gaming system
193 owned an iPod and laptop
200 owned an iPod and gaming system
139 owned a laptop and a gaming system
68 owned an iPod, laptop and gaming system
26 owned none of these devices
Of the college students surveyed, how many owned a) exactly two of these devices b) at least one of these devises
I am not sure if I am supposed to figure out how many students were surveyed to be able to solve this or what.
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! It looks like all of the students were surveyed. Otherwise,
you couldn't solve it.
Draw three interlocking rings ( Venn diagram ) so that
there is an area in the center which is common to
all three rings.
---------------
It's helpful to notice there are 8 categories listed and the
Venn diagram divides into 7 areas. Everything outside
the 3 rings is the last category:
" 26 owned none of the devices"
---------------------------
The area in the center is:
"68 owned an iPod, laptop and gaming system"
Now there are 6 categories left
--------------------------
"193 owned an iPod and laptop"
If you subtract 68, you get 125, which is the area
( ipod + laptop ), but not ( ipod + laptop + gaming system )
---------------------------------------------------
"200 owned an iPod and gaming system"
If you subtract 68, you get 132, which is the area
( ipod + gaming system ), but not ( ipod + laptop + gaming system )
----------------------------------------------------------
"139 owned a laptop and a gaming system"
If you subtract 68, you get 71, which is the area
( laptop + gaming system ), but not ( ipod + laptop + gaming system )
------------------------------------------------------------
Now there are 3 categories left
"356 owned an iPod"
Now subtract ( 125 + 68 + 132 = 325 )
356 minus 325 = 31
These 31 own an ipod and nothing else
---------------------------------
"293 owned a laptop"
subtract { 71 + 68 + 125 = 264 )
293 minus 264 = 29
29 own a laptop and nothing else
-----------------------------
"285 owned a gaming system"
subtract ( 132 + 68 + 71 = 271 )
285 minus 271 = 14
14 own a laptop and nothing else
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(a)
The number that owned exactly 2 of the devices is
( 125 + 132 + 71 = 328 )
(b)
The number that owned at least 1 of the devices is
The sum of all the areas:
( 14 + 29 + 31 + 71 + 125 + 132 + 68 = 470 )
Hope I got it
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