Chap 2: Axioms of Probability
Motivating Example:
EX: A 5-card poker hand is said to be a full house if it consists of 3 cards of the same
denomination and 2 cards of the same denomination. (That is, a full house is three of a kind
plus a pair.) What is the probability that one is dealt a full house?
2.2 Sample Space and Events
A pair of concepts
Sample space: the set of all possible outcomes of an experiment. Denoted by S.
Event: any subset of the sample space is know as an event. Denoted by E.
EX: First row a die, then toss a coin. What is the sample space?
Example on textbook. (bkpg 22-23)
Union, Intersection, and Complement
1. union: E U F
2. Intersection: E ∩ F
3. Complement: Ec
Venn diagram:
Example: The following table summarizes visitors to a local amusement park:
One visitor from this group is selected at random:
1) Define the event A as “the visitor purchased an all-day pass”
2) Define the event B as “the visitor selected purchased a half-day pass”
3) Define the event C as “the visitor selected is female”
Describe the relationship and draw Venn diagram.
Rules for operation of forming Unions, Intersections, and Complements:
1. Commutative laws: E U F = F U E, E ∩ F = F ∩ E
2. Associative laws: ( E U F ) U G = E U ( F U G ), ( E ∩ F ) ∩ G = E ∩ ( F ∩ G )
3. Distributive laws: ( E U F ) ∩ G = ( E ∩ G ) U ( F ∩ G )
4. DeMorgan’s laws:
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All-Day Half-Day
Pass Pass Total
Male 1200 800 2000
Female 900 700 1600
Total 2100 1500 3600
