problem set

Question

In a survey, 110 freshmen of San Pedro were asked on their preferred network SIM. The result was: 66 used Smart
49 used Globe
26 used Sun Cellular
28 used Smart and Globe
12 used Globe and Sun Cellular
13 used Smart and Sun Cellular
9 used Smart, Globe and Sun Cellular

How many use:

a. Smart sim only? Globe sim only?

b. Sun cellular sim only?

c. neither of the three sims?

d. exactly two of the sims?

e. at least two of the sims?

f. at most two of the sims?

Answer 1

here the words plays very important role...'and' represents 'intersection'  .with venn diagram its very easy to find all the ans but here i cant draw it...you can take the help of follwing symbolic form and draw the venn diagram

 

i am going to use letters..

A for Smart sim users

B for Globe sim users

C for Sun cellular sim users 

 

whatever is given write in symbolic form

66 used Smart :          A= 66

49 used Globe  :          B= 49

26 used Sun Cellular : C= 26

28 used Smart and Globe : AnB =28

12 used Globe and Sun Cellular: BnC =12

13 used Smart and Sun Cellular: AnC =13

9 used Smart, Globe and Sun Cellular: AnBnC = 9

So, used neither of the three sims =110- (A∪B∪C) =110-97 =13  [(A∪B∪C) is easy to find with the help of venn diagram)

 

a. smart sim only =34 , globe sim only = 18

b. Sun cellular sim only= 10

c. neither of the three sims=13
d. exactly two of the sims = 26
e. at least two of the sims= 35
f. at most two of the sims = 101