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) both subjects
b) at least one of the subjects
c) Physics, but not Chemistry
d) Exactly one of the subjects
e) Neither subject
f) 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) play hockey
b) play both sports
c) play neither sport
d) 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