Question 1201039
<font color=black size=3>
This is one way to have a starting Venn Diagram template.
{{{
drawing(400,300,-2,10,-2,8,
line(1,1,1,6),line(1,6,8,6),line(8,6,8,1),line(8,1,1,1),

circle(3.64,3.44,2),circle(5.64, 3.44,2),

locate(7.2,8,matrix(1,3,"M","=","math")),
locate(7.2,7.5,matrix(1,3,"E","=","English")),

locate(1.84,5.34,M),
locate(6.76,5.82,E),
locate(2.6,4,a),
locate(4.38,4,b),
locate(6.26,4.24,c),
locate(6.9,1.82,d)
)
}}}
M = set of freshmen taking math (some also taking English)
E = set of freshmen taking English (some also taking math)
region a = freshmen taking math only
region b = freshmen taking both math and English
region c = freshmen taking English only
region d = freshmen taking neither course


Let's say there are 1000 freshmen as a hypothetical situation.


Given facts
<table border = "1" cellpadding = "5"><tr><td>Number</td><td>Statement</td></tr><tr><td>1</td><td>39% of freshmen are enrolled in </br>both a math course and an English course</td></tr><tr><td>2</td><td>11% are enrolled in a math course, </br>but not an English course</td></tr><tr><td>3</td><td>63% are enrolled in an English course</td></tr></table>
Fact 1 means there are 0.39*1000 = 390 freshmen enrolled in both math and English. 
This value will replace "b" in the Venn Diagram above.


Fact 2 means there are 0.11*1000 = 110 freshmen enrolled in math, but not in English. 
This value will replace "a" in the Venn Diagram above.


Fact 3 means there are 0.63*1000 = 630 freshmen enrolled in English (some of these students may also be in math). 
Subtract off the amount of freshmen taking both to get 630-390 = 240. 
This is the number of freshmen taking English only.
This value replaces the "c" in the Venn Diagram above.


This is what you should have so far.
{{{
drawing(400,300,-2,10,-2,8,
line(1,1,1,6),line(1,6,8,6),line(8,6,8,1),line(8,1,1,1),

circle(3.64,3.44,2),circle(5.64, 3.44,2),

locate(7.2,8,matrix(1,3,"M","=","math")),
locate(7.2,7.5,matrix(1,3,"E","=","English")),

locate(-1,8,matrix(1,2,"Hypothetical","Scenario:")),
locate(-1,7.5,matrix(1,3,"1000","freshmen","total")),

locate(1.84,5.34,M),
locate(6.76,5.82,E),
locate(2.6,4,110),
locate(4.38,4,390),
locate(6.26,4.24,240),
locate(6.9,1.82,d)
)
}}}
The a,b,c was replaced with 110, 390, and 240 in that exact order.
The amount of freshmen so far is 110+390+240 = 740


Since there are 1000 freshmen total, we know that 1000-740 = 260 freshmen aren't taking math and aren't English either. 
This value will replace "d" in the diagram.


Here's the final Venn Diagram
{{{
drawing(400,300,-2,10,-2,8,
line(1,1,1,6),line(1,6,8,6),line(8,6,8,1),line(8,1,1,1),

circle(3.64,3.44,2),circle(5.64, 3.44,2),

locate(7.2,8,matrix(1,3,"M","=","math")),
locate(7.2,7.5,matrix(1,3,"E","=","English")),

locate(-1,8,matrix(1,2,"Hypothetical","Scenario:")),
locate(-1,7.5,matrix(1,3,"1000","freshmen","total")),

locate(1.84,5.34,M),
locate(6.76,5.82,E),
locate(2.6,4,110),
locate(4.38,4,390),
locate(6.26,4.24,240),
locate(6.9,1.82,260)
)
}}}
As a check:
a+b+c+d = 110+390+240+260 = 1000


=============================================================


Now to answer the questions.


Problem 1) <font color=blue>What is the probability that a freshman student selected at random is taking an English course but not a mathematics course?</font>


Refer to the Venn Diagram above.
We see there are 240 freshmen taking English but not math. 
This is out of 1000 freshmen total.
240/1000 = 0.24


Answer: <font color=red>0.24</font>


------------------------------------


Problem 2) <font color=blue>What is the probability a student is not enrolled in either course?</font>


Refer to the Venn Diagram above.
There are 260 freshmen that aren't taking either course mentioned. 
This is out of 1000 freshmen total.


260/1000 = 0.26


Answer: <font color=red>0.24</font>
</font>