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
Venn with 3 sets:
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:
---------------
A student has competed in none of the categories?
Probability = 
A student has competed in Smooth, Rhythm, or Standard? is it .4266055046??
Probability = 
A student has competed in Smooth or Standard, but not Rhythm?
Probability = 
A student has competed in Rhythm and Standard, but not Smooth?
Probability = 
A student has competed in Rhythm, given you know the student has competed in
Smooth.
Probability = 
Edwin
