- In a class of 31 students 17 are studying art and 14 are studying dance. Five students’ study neither of these subjects.
(a) How many students study both?
(b) What is the probability that a randomly selected student studies art?
(c) What is the probability that a randomly selected student studies art and not dance?
When you fill in the Venn Diagram, the first data you would input would be the 5 students that study neither. (In any question which requires a Venn Diagram, this is always the first step to be taken).
You don't know how many students study both art and dance. So in the middle, you need to write x (or any letter) - Then use algebra to write in terms of x how may students study only dance, and how many students study only art.
Add all of the 3 algebra expressions (the number of students studying both, the number of students studying just dance, and the number of students studying just art) - you equal that to 26 because 5 students study neither. Work out what x is, then re-draw your venn diagram, but this time with the actual values, instead of an algebraic expression.
This method will then help you answer all the question above.