PIB Geometry
Probability 3:
Venn Diagrams
Warm Up
Given a dozen eggs, Mr. Cawelti hard-boiled 4 of them and
placed them back in the carton. He then forgot which ones
were which. If he chooses 2 eggs at random, what is the
probability that exactly 1 of them will be hard boiled? Draw a
tree diagram to help you visualize.
Venn Diagrams!
Notation:
• 𝐴∪𝐵
• 𝐴∩𝐵
The diagram shows how many students in a class
play baseball (B), and how many play tennis (T).
What is T ∪ 𝐵? T ∩ 𝐵?
The size of sets

In a class of 50 students, 23 like geometry, 22 like
algebra, and 20 like neither. Complete the Venn
diagram
You try!
In a group of 40 students, 22 study economics, 25 study law, and
3 study neither. Draw a Venn diagram to model the situation.
Determine the probability that a randomly chosen student
studies:
1. Both economics and law
2.
Economics, given that s/he studies law
Addition Law of Probability
𝑃 𝐴∪𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃 𝐴∩𝐵
Or in other words…
𝑃 𝐴 𝑜𝑟 𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)
Ex) What is the probability that a number between
1 and 20 is a multiple of 3 or 4?
Example
In a 52-card deck, what is the probability
that a randomly selected card is a face card
or a red card?
What is wrong with this picture?