T 102  Worksheet Using Venn Diagrams to Solve Problems                  NAME____________

 

DIRECTIONS:  Use Venn diagrams to answer each of the following questions.  You

   must show your Venn diagram for each problem.

 

  1. A survey of 80 sophomores at a certain western college showed the following:

 

36 take English                                     32 take history

32 take political science                                    16 take history and English

16 take political science and history                   14 take political science and English

 6 take all three

           

            How many students:

                        a) take English and neither of the other two?                  ____________

 

                        b)  Take none of the three courses?                               ____________

 

                        c)  take history, but neither of the other two?                 ____________

 

d)      take political science and history but not English?____________

 

e)  do not take political science?                                    _____________

 

 

  1. The following list shows the preference of 102 people at a wine-tasting party:

 

99 like Spanada                                                94 like Ripple and Boone’s

96 like Ripple                                                   96 like Spanasa and Boone’s

99 like Boone’s Farm Apple Wine                    93 like all three

95 like Spanada and Ripple

 

How many people prefer:

 

            a)  none of the three?                                                    ______________

 

            b)  Spanada, but not Ripple?                                         ______________

 

            c)  anything but Boone’s Farm?                         ______________

 

            d)  exactly two kinds of wine?                           ______________

 

  1. A chicken farmer surveyed his flock with the following results.  The farmer

Has:

            9 fat red roosters(male) 37 fat chickens 6 thin red roosters

            2 fat red hens                            7 thin brown hens         5 thin red hens

            26 fat roosters (total)                18 thin brown roosters

Answer the following questions about the flock(HINT: in your Venn diagram make a circle for fat, for male and for red).  How many chickens are:

 

            a)  fat?  __________    b)  red?  ___________       c)  male?   _________

 

            d)  fat, but not male?  _________             e)  brown, but not fat?  ________

 

e)      read and fat?  _________

 

 

  1. Country-Western songs emphasize three basic themes: love, prison and trucks.  A

survey or the local Country-Western radio station produced the following data:

 

12 songs about a truck driver who is in love while in prison

2 about people in prison who are not in love and do not drive trucks

8 about people who are out of prison, are not in love, and do not drive a truck

13 about a prisoner in love

28 about a person in love

18 about a truck driver in love

16 about truck drivers who are not in prison

3 about a truck driver in prison who is not in love

 

Find the number of songs about:

 

            a)  How many songs were surveyed?    _________b)  truck drivers?    ______

 

            c)  prisoners?                __________    d)  truck drivers in prison?        ______

 

            e)  people not in prison?            __________f)  people not in love?       ______

 

  1. In a certain hospital, the following data on patients were recorded:

 

25 patients had the A antigen                            30 had the Rh antigen

17 had the A and the B antigen             12 had none of the antigens

27 had the B antigen                                         16 had the A and Rh antigen

22 had the B and Rh antigens                            15 had all three antigens

 

How many patients:

 

            a)  are represented here?          _________

 

            b)  have exactly one antigen?                 __________

 

            c)  have exactly two antigens?   ________

 

 

ANSWERS

1.  a.  12          b.  20   c.  6     d.  10   e.  48

2.  a.  0                        b.  4     c.  3     d.  0     e.  6

3  a.  37           b.  22   c.  50   d.  11   e.  25   f.  11

4  a.  51           b.  31   c.  18   d.  15   e.  33   f.  23

4  a.  54           b.  17   c.  10