By the end of this section you should be able to: ● represent a word problem in a Venn diagram ● use Venn diagrams to solve word problems
Venn diagram word problems generally give you two diff erent sets and and some information about each set. You then have to use the given information to draw a Venn diagram and fi gure out the remaining information.
Worked example 1:
when you know the value in the intersection In a group of 40 students, 14 study German and 29 study Physics. There are fi ve students who study both German and Physics.
(i) Draw a Venn diagram to represent this information. (ii) How many students study neither subject? (iii) How many students study only one subject? (iv) How many students study German only? (v) What is the probability that a randomly-chosen student from this group is only studying Physics?
Solution (i)
Always fi ll in the intersection information fi rst.