Problema Solution
in a survey of 60 people, it was found that 25 read Newsweek magazine, 26 read Time and 26 read Fortune. Also, 9 read both Newsweek and Fortune, 11 read both Newsweek and time , 8 read both time and fortune and 8 read none of these.
find the number of people who read all the three magazines
draw a venn diagram and fill in the correct number of readers in each of the regions
determine the number of people who read exactly one magazine
Answer provided by our tutors
we introduced the set U of all surveyed people anf its substes N ,T ,F who reads news week, time , fortune .
the condition of problem can be wrriten as
n(U)=60
n(N)= 25
n(T)= 26
n( F)= 25
n( N INTERSECTION F)= 9
n( N INTERSECTION T)=11
n( F INTERSECTION T) =8
n( N INTERSECTION T INTERSECTION F)= 8
NOW WE CAN USE THE FORMAULE
n( N UNION T UNION F)= n(N) +n(T)+n( F) -n( N INTERSECTION F) -n( N INTERSECTION T)-n( F INTERSECTION T) +n( N INTERSECTION T INTERSECTION F) -------1
n( N INTERSECTION T INTERSECTION F)+n( N UNION T UNION F) = 60
n( N UNION T UNION F)= 60 -8=52
USE ABOVE IN EQUATION 1
WE GETS
n( N INTERSECTION T INTERSECTION F)= 4
. From the Venn diagram we see that the number of people reading exactly one of
these two magazines is 9 1+ + = 1 12 32 .
FROM VENN DIAGRAM
number of people who read exactly one magazine=9+11+12=32