Question 1067713
<pre>
You should begin by making a complete Venn diagram with 2 sets.

Start with the 8 in the middle region which take both ballet and
tap.  Then do as you did and subtract 8 from the 50, getting
42 who take ballet only.  Then subtract the same 8 from 24, getting
16 who take tap only.  Then find the number who take ballet or tap
or both 42+8+16 = 66.  Then since there are 100 students in all,
that means that 100-66 = 34 do not take either ballet or tap. (I
suppose they take ballroom dancing or jazz). Put those 34 outside
both circles.  I put it in the bottom left corner of the rectangle.
 
{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,42),locate(1.5,1.7,16),locate(-3.7,-1,34), locate(-3.6,2.5,B), locate(-.1,1.8,8),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,T)
 )}}}

Now to get the desired conditional probability, find the reduced
sample space by erasing all the tap dancers. 

{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,42),locate(-3.7,-1,34), locate(-3.6,2.5,B),

red(arc(-sqrt(2),sqrt(2),4,-4-1.2,45,315)),
red(arc(-sqrt(2),sqrt(2),3.9,-3.9-1.2,45,315)),
red(arc(-sqrt(2),sqrt(2),3.95,-3.95-1.2,45,315)),

blue(arc(sqrt(2),sqrt(2),4,-4-1.2,135,225),
arc(sqrt(2),sqrt(2),3.9,-3.9-1.2,135,225),
arc(sqrt(2),sqrt(2),3.95,-3.95-1.2,135,225))
 )}}}

Now the reduced sample space contains only 42+34 or 76.  
So the conditional probability is 42 out of 76 or 42/76 
which reduces to 21/38. 

Edwin</pre>