Question 854691
<pre>
A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories:
A: Smooth
B: Rhythm
C: Standard
The results were then presented to the owner in the following Venn Diagram.
d is Smooth ONLY (NOT RHYTHM, NOT STANDARD)
h is Rhythm ONLY (NOT SMOOTH, NOT STANDARD)
j is Standard ONLY (NOT SMOOTH, NOT RHYTHM)
e is Smooth and Rhythm ONLY (NOT STANDARD)
g is Smooth and Standard ONLY (NOT RHYTHM)
i is Rhythm and Standard ONLY (NOT SMOOTH)
f is Smooth,Rhythm,Standard (ALL THREE)
k is none
<pre>
 Venn with 3 sets:
{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2,2,d),
locate(3.5,-2,k)
locate(0,-2.7,C),
locate(-.3,-1,j),
locate(1.1,.4,i), 
circle(sqrt(2),sqrt(2),2), 
locate(-3.5,2.5,A),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,B),
locate(-1.3,.5,g),
locate(0,2.5,e),
locate(2,2,h),
locate(-.2,1.1,f) )}}}


There were d+e+f+g+h+i+j+k students in the survey.

If a student is chosen at random, what is the probability that:
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A student has competed in none of the categories?

Probability = {{{k/(d+e+f+g+h+i+j+k)}}}

A student has competed in Smooth, Rhythm, or Standard? is it .4266055046??
<pre>

Probability = {{{(d+e+f+g+h+i+j)/(d+e+f+g+h+i+j+k)}}}

A student has competed in Smooth or Standard, but not Rhythm?

Probability = {{{(d+g+j)/(d+e+f+g+h+i+j+k)}}}

A student has competed in Rhythm and Standard, but not Smooth?

Probability = {{{i/(d+e+f+g+h+i+j+k)}}}

A student has competed in Rhythm, given you know the student has competed in
Smooth. 

Probability = {{{(e+f)/(d+e+f+g)}}}

Edwin</pre>