Kelly interviewed 75 customers at Borders about their magazine subscriptions. The revealed the following information:
32 had a subscription to Fortune
20 had a subscription to Newsweek
23 had a subscription to Time
9 had a subscription to Fortune and Newsweek
13 had a subscription to Fortune and Time
5 had a subscription to Newsweek and Time
4 had a subscription to all three magazines
Kelly’s supervisor wants to know how many customers subscribed to Fortune or Time magazine. Can this information be determined from Kelly’s report? If so, find the number of customers that subscribed to Fortune or Time magazine.
construct a Venn diagram with three overlapping circles, labeled F, N, and T for the 3 magazines
Fill in form the centre outwards, that is, place 4 in the intersection of all 3
9 in the intersection of only the F and T overlaps, (9+4 = 13)
etc
Fortune OR time would be the total of all the different part except those that subscribe to ONLY N
To find out how many customers subscribed to Fortune or Time magazine, we need to use the principles of set theory and the concept of inclusion-exclusion principle.
Given the information provided, we can create a Venn diagram to represent the subscriptions:
```
__________
/ \
Fortune / \ Time
________/______________\
| |
|______________|
Newsweek
```
Let's assign variables to the different sets:
- Let "F" represent the set of customers subscribed to Fortune.
- Let "N" represent the set of customers subscribed to Newsweek.
- Let "T" represent the set of customers subscribed to Time.
Now let's apply the information we have:
- The number of customers who subscribed to Fortune, N(F) = 32.
- The number of customers who subscribed to Newsweek, N(N) = 20.
- The number of customers who subscribed to Time, N(T) = 23.
- The number of customers who subscribed to both Fortune and Newsweek, N(F ∩ N) = 9.
- The number of customers who subscribed to both Fortune and Time, N(F ∩ T) = 13.
- The number of customers who subscribed to both Newsweek and Time, N(N ∩ T) = 5.
- The number of customers who subscribed to all three magazines, N(F ∩ N ∩ T) = 4.
Now we can use the inclusion-exclusion principle to find the number of customers who subscribed to Fortune or Time:
N(F ∪ T) = N(F) + N(T) - N(F ∩ T)
Using the values we have:
N(F ∪ T) = 32 + 23 - 13
N(F ∪ T) = 42
So, based on Kelly's report, we can determine that 42 customers subscribed to Fortune or Time magazine.