How do I use Venn Diagrams to solve probability problems?
Notes # ___________
Probabilities using Venn Diagrams
Ex 1: In a class of 30 students, 19 study physics, 17 study Chemistry, and 15 study both of these subjects. Display this
information on a Venn diagram and hence determine the probability that a random selected class member studies:
a)
b)
c)
d)
e)
f)
both subjects
at least one of the subjects
Physics, but not Chemistry
Exactly one of the subjects
Neither subject
Chemistry if it is known that the student studies Physics
Ex 2: In a particular sports club, 42 students play tennis, 53 students play field hockey, and 27 students play both and 7 play
neither. Use a Venn diagram to determine the probability of the number of people that :
a)
b)
c)
d)
play hockey
play both sports
play neither sport
play at least one sport
You Do: In a class of IB students, many of the students study music, drama, or physics. 14 study drama, 15 study music, and
10 study physics. 6 study drama and physics, 5 study music and physics, 6 study music and drama, and 4 students study all
3. Find the probability that a student studies:
a) physics
b) Music or drama but not both
c) Study Physics but not music
d) Does not study drama