Venn Diagrams can be a useful tool to represent and solve probability questions
Sample space: All possible outcomes of an experiment
Union(∪, "or"): A∪B is the event that either A occurs or B occurs or they both occur
Intersection (∩, “and”): A∩B is the event that both A occurs and B occurs
Addition Rule: A shortcut formula to finding is: A∪B = A + B – A∩B
Complement (Ac): All outcomes EXCEPT the event P(Ac)=1−P(A)
Venn Diagrams Represent Events
Out of a school of 100 students the number of students enrolled in PE and Band class is given below:
So there are 35 students who are taking only PE classes, 30 students who are taking only Band classes, and 20 students who are taking both PE and Band classes. There are also 15 students who are not enrolled in PE or Band classes.
Union and Intersection with Venn Diagrams
The following dots represent students who attend each after school activity:
From a deck of cards 10 cards are drawn at random. From these 10 cards the probability of picking a king is 0.3 and the probability of picking a heart is 0.5. The probability of picking a card that is both a king and a heart (the king of hearts) is 0.1.
Determining the Complement of Events
The probabilities of certain events are given in the Venn Diagram below:
Probability with Venn diagrams
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We have 1107 practice questions in Algebra 2 for you to work through.