1)100 people surveyed, top two answers on the board ...

" ... if 68 people like Oh Henry and 45 like Snickers ..."

a) ... what is the minimum and maximum number of people that like both of these chocolate bars?

b) ... what is the minimum and maximum number of people that like neither of these chocolate bars?

Use a Venn diagram to help you find these ranges of values.

a) the minimum and maximum number of people that like both of these chocolate bars are 13 and 45 respectively

b) the minimum and maximum number of people that like neither of these chocolate bars are 0 and 32 respectively

I hope this helps

Step-by-step explanation

I'll give you an orientation:

We have two sets:

A = {people that like Snickers}

B = {people that like Oh Henry}

The minimum size of ?A∩B? is gotten assuming that A and B are disjoint, but we cannot assume this since the sum of the size of the sets (68 + 45) is greater than the size of the universe (100). So,

?n(A∩B)=65+48−100=13?

The maximum size of ?A∩B? is gotten assuming that a set is contained into another set. In this case the set A is contained into the set B. Then, ?n(A∩B)=n(A)=45?

Now, the minimum size of ?A∩B? is the maximum size of ?Ac∩Bc? and vice-versa (?Ac∩Bc? means people that like neither of these chocolate bars)

By De Morgan's law: ?Ac∩Bc=(A∪B)c?

?A∪B=65+48−13=100? then ?(A∪B)c? is 0 (minimum size of ?Ac∩Bc?)

If ?A⊂B? then ?(A∪B)c=Bc? and the size of this set is 100 - 68 = 32 (the size of B is 68)