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.
 


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



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