A study was made of 200 preschoolers to determine if they watched some particular television shows. The choices were Little Galileo, Super Reader and Prehistoric Train. The results are

I. 22 preschoolers did not watch any of these shows
II. 73 preschoolers only watched Little Galileo
III. 136 preschoolers watched Little Galileo
IV. 14 preschoolers only watched Super Reader and Prehistoric Train
V. 31 preschoolers only watched Little Galileo and Prehistoric Train
VI. 63 preschoolers watch Super Reader
VII. 135 preschoolers do not watch Prehistoric Train
Choose the following statements about the probabilities of preschool television viewing that are correct.

68% of the preschoolers watched Little Galileo
31.5% of preschoolers do NOT watch Super Reader
67.5% of preschoolers only watch Prehistoric Train.
89% of the preschoolers watch Little Galileo, Super Reader, or Prehistoric Train.
35.4% of preschoolers who watch a show watch Super Reader.
22% of preschoolers do NOT watch Little Galileo, Super Reader or Prehistoric Train.
7% of preschoolers only watch Prehistoric Train and Super Reader.
23.6% of preschoolers who watch a show watch Little Galileo.
68.5% of the preschoolers do NOT watch Super Reader
75.8% preschoolers who watch a show, do NOT watch Prehistoric Train.

2 answers

Draw your Venn diagram. If
x = # who watched Galileo & Reader
y = # who watched all three shows
t = # who watched only Train
r = # who watched only Reader
then we know that
73+x+y+31 = 136
x+y+r+14 = 63
73+x+r+22 = 135
73+x+r+y+31+14+t = 200-22
Simplifying all those, we get
x+y = 32
x+y+r = 49
x+r = 40
x+y+r+t = 60
Now we can substitute x+r=40 and x+y=32, to get
r = 17
y = 9
t = 11
so, x = 23
Now you can check the statements
what is the answer