Question 1197041: A survey of 95 persons was conducted at PCC. Everyone was asked if they carried a cell phone and they were asked if they carried a tablet. It was found that 38 persons carried a cell phone, 19 persons carried a tablet computer, and 9 carried both a cell phone and a tablet.
Remember to draw a Venn Diagram to help you answer this question.
How many people carried a cell phone or a tablet?
Hint: You might want to determine how many people carried JUST a cell phone or JUST a tablet. Make sure the four regions of your set diagram add to 95.
How many people carried neither a cell phone nor a tablet?
How many people carried a cell phone only?
How many people carried a tablet but not a cell phone?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
C = set of people who have a cell phone
T = set of people who have a tablet
Given Info:
95 total people surveyed
38 persons carried a cell phone
19 persons carried a tablet computer
9 carried both a cell phone and a tablet
This is what the Venn diagram looks like.
Here's the process to getting those values in red.
9 people have both a cell phone and tablet, so we write "9" without quotes in the overlapped region of the two circles C and T.
Since 9 people had both, and 38 have a cell phone, this means 38-9 = 29 people have a cell phone only.
Write "29" inside circle C, but outside circle T
Since 9 people had both, and 19 have a tablet, this means 19-9 = 10 people have a tablet only.
Write "29" inside circle T, but outside circle C
We have:
29 people with a cell phone only
10 people with a tablet only
9 people with both
This accounts for 29+10+9 = 48 people.
The remaining 95 - 48 = 47 people have neither cell phone nor tablet. We'll write "47" outside both circles but inside the universal rectangle set.
The universal set in this case refers to the 95 people surveyed.
As a check, add up all the red numbers in the entire venn diagram 29+9+10+47 = 95 and it helps confirm we have the correct values. This is what your teacher refers to when s/he says "Make sure the four regions of your set diagram add to 95".
We'll use that venn diagram to answer the questions below.
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Question: How many people carried a cell phone or a tablet?
Answer: 48
Reason: Add the numbers up that are in either circle
29+9+10 = 48
Or you can subtract the number of people who don't have either device from the grand total
95 - 47 = 48
Another approach could be this
n(C or T) = n(C) + n(T) - n(C and T)
n(C or T) = 38 + 19 - 9
n(C or T) = 48
notation like n(C) means "the number of people in set C", i.e. "the number of people who have cell phones".
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Question: How many people carried neither a cell phone nor a tablet?
Answer: 47
Reason: This was the number mentioned outside of both circles.
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Question: How many people carried a cell phone only?
Answer: 29
Reason: Refer to the value inside circle C but outside circle T.
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Question: How many people carried a tablet but not a cell phone?
Answer: 10
Reason: Refer to the value inside circle T but outside circle C.
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