Question 1199830
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Draw a rectangle to represent the universal set.
Inside the rectangle, draw partially overlapping circles which I'll label as R and S.


R = set of people who read the book
S = set of people who saw the movie


{{{drawing(400,200,-10,10,-10,10,
circle(-2,1-1,4),
circle(2,1-1,4),
locate(-5,9-1,"R"),
locate(5,9-1,"S"),
line(-8,9.6,8,9.6),
line(8,9.6,8,-9.6),
line(-8,-9.6,8,-9.6),
line(-8,9.6,-8,-9.6)
)}}}


Now write "2" without quotes in the overlapped region of the circles.
{{{drawing(400,200,-10,10,-10,10,
circle(-2,1-1,4),
circle(2,1-1,4),
locate(-5,9-1,"R"),
locate(5,9-1,"S"),
locate(0,2-1,"2"),
line(-8,9.6,8,9.6),
line(8,9.6,8,-9.6),
line(-8,-9.6,8,-9.6),
line(-8,9.6,-8,-9.6)
)}}}
These are the 2 people who read the book and saw the movie.


8 people read the book, and 2 did both, which means 8-2 = 6 read the book but didn't see the movie. 
This value goes in circle R but outside circle S.


5 people saw the movie, and 2 did both, which means 5-2 = 3 saw the movie but didn't read the book. 
This value goes in circle S but outside circle R.


Let's update the diagram
{{{drawing(400,200,-10,10,-10,10,
circle(-2,1-1,4),
circle(2,1-1,4),
locate(-5,9-1,"R"),
locate(5,9-1,"S"),
locate(-4,2-1,"6"),
locate(4,2-1,"3"),
locate(0,2-1,"2"),
line(-8,9.6,8,9.6),
line(8,9.6,8,-9.6),
line(-8,-9.6,8,-9.6),
line(-8,9.6,-8,-9.6)
)}}}
Side notes:<ul><li>The values in circle R add to 6+2 = 8 who read the book.</li><li>The values in circle S add to 2+3 = 5 who saw the movie.</li></ul>Add the values in the circles: 6+2+3 = 11
There are 11 people who read the book, saw the movie, or both.


16 total people are present. It tells us 16-11 = 5 people did not read the book nor did they see the movie.


The "5" will go outside both circles, but stay inside the universal set.


Final Venn Diagram
{{{drawing(400,200,-10,10,-10,10,
circle(-2,1-1,4),
circle(2,1-1,4),
locate(-5,9-1,"R"),
locate(5,9-1,"S"),
locate(-4,2-1,"6"),
locate(4,2-1,"3"),
locate(0,2-1,"2"),
locate(-7,0-1,"5"),
line(-8,9.6,8,9.6),
line(8,9.6,8,-9.6),
line(-8,-9.6,8,-9.6),
line(-8,9.6,-8,-9.6)
)}}}


The goal is to select someone who hasn't seen the movie nor read the book. There are 5 such people out of 16 total.
This forms the probability 5/16.



Answer: <font color=red size=4>5/16</font>
5/16 = 0.3125 when converting to decimal form. This value is exact without any rounding done to it.
0.3125 = 31.25%
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