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I drew a venn diagram but I am still trying to figure out the answers. Any help?

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    Well, I have tried on this question and keep failing.. – 2017-01-27
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    Add pic of Venn diagram. – 2017-01-27

4 Answers 4

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Start with the $3$ people in the all-phones zone and add people into the 2-phone zones to make up the given total. For example, of the $8$ people who own Blackberry and Android, $3$ also own an iPhone, leaving $5$ additional to go into that 2-phone area. Then work out to the single-phone sets and finally the "none of the above" set.

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    Still can't figure out this out, what am i doing wrong – 2017-01-27
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    @keving we don't know what you are doing wrong if we don't see what it is that you are doing. – 2017-01-27
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An approach which doesn't use venn diagrams and is a more pen-and-paper "mathy" method, but might work better for you depending on how your mind works:

Let $A$ be the set of people who own androids (and possibly other devices too)

Let $B$ be the set of people who own blackberries (and possibly other devices too)

Let $I$ be the set of people who own iPhones (and possibly other devices too)

Inclusion-exclusion states that

$$|A\cup B\cup I|=|A|+|B|+|C|-|A\cap B|-|A\cap I|-|B\cap I|+|A\cap B\cap I|$$

And we know further that $|A^c\cap B^c\cap I^c|=|\Omega|-|A\cup B\cup C|$

Each of the numbers required to calculate $|A^c\cap B^c\cap I^c|$ (i.e. the answer to part (a)) are given in the problem statement and you need only plug in the numbers and complete the required arithmetic.

$|A| = 30, |A\cap B|=8, |A\cap B\cap I|=3,\dots$

Similar uses of inclusion-exclusion and addition principle can help you work out the remaining desired information.

For example, $|B\cap I^c| = |B|-|B\cap I|$

what seems to confuse many beginners about this unit is the phrasing. The phrase "12 owned an android and an iphone" means that $12$ people own an android and an iphone and possibly a blackberry too, it is not that $12$ people own an android and an iphone and not a blackberry.

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Hint: For each overlapping region, subtract the number from its outside regions. For example, subtract $3$ from the iPhone, Blackberry, and Android counts.

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a.) None owned any 3 phones -

300 - Sum of all numbers in venn diagram.

b.) People owned blackberry = sum of all values in blackberry circle (except intersection of blackberry and iPhone).

c.) People owned blackberry = sum of all values in blackberry circle (except intersection of blackberry and android).