Lec 5 - Introduction to probability
STAT 1010 - Fall 2022
By the end of this lesson you should:
Understand probability and its axioms
Know and understand words like union, intersection, and compliment
Be able to calculate basic probabilities
History of probability
- Gives you an edge in games of chance
- Cardano, Fermat, Pascal, Kolmogorov
- casinos rely on probability theory for profits
Word cloud of probability
Use this link, or the qr code below
- An experiment is a process that produces an observation.
- An outcome is a possible observation.
- The set of all possible outcomes is called the sample space.
- An event is a subset of the sample space.
- A trial is a single running of an experiment.
- Events are disjoint or mutually exclusive if they have no outcomes in common.
Roll a fair, 6-sided and observe the number of pips that appear on top.
- What is one outcome of a trial?
- What is the sample space?
- What are possible events?
- What are some disjoint events?
- What are the probabilities of the events above?
The 3 axioms of probability
- The probability of the sample space (\(S\)) is 1 (ie \(P(S) = 1\))
- A probability \(p\) is always between \(0\) and \(1\) (ie \(0 \leq p \leq 1\))
- If two events \(A\) and \(B\) are disjoint, then \(P(A \cup B) = P(A) + P(B)\)