Answer/Discussion
to 4a - 4c
A group of students were asked if they liked rock or
country music.
The results were as follows: 27 said they liked rock, 20 said they
liked
country, 5 liked both, and 3 liked neither.
The first thing we need to do is draw a Venn diagram
with two adjoining
circles - one for rock and one for country.
Now we need to fill in numbers into the correct regions
based on the
information that was given.
We need to start with something
that only goes
with one region and then work our way out from that.
Two statements deal with only one region. If more
than one does,
it doesn't matter the order you fill them in as long as they go with
only
one area.
It says that 5 liked both. The only region that
both circles meet
in is region II, so we will have to put a 5 there.
Another statement that pertains to only one region is 3
like neither.
That means we will be putting the number 3 in region IV.
Let's put those into our Venn diagram and see what is
left:
Looks like we still need to fill in regions I and
III.
It says that 27 said they liked rock - the rock circle
is composed of
regions I and II. Since II already had 5, then region I is
going
to have to be 27 - 5 = 22.
It also says that 20 said they liked country - the
country circle is
composed of regions II and III. Since II already has 5,
then region
III is going to have to be 20 - 5 = 15.
Final answers:
4a. How many students chose only rock?
This would be region I.
The number of students that chose only rock is
22. |
4b. How many students chose only country?
This would be region III.
The number of students that chose only country
is 15. |
4c. How many students were surveyed?
This would be regions, I, II, III, and IV.
To find the total we simply add up all the
regions: 22 + 5 + 15 + 3
= 45
The number of students that were interviewed
about rock and country
is 45. |
(return
to problem
4) |