Lec 5 - Introduction to probability

STAT 1010 - Fall 2022

Learning outcomes

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

Basic terminology

• 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.

An experiment

Roll a fair, 6-sided and observe the number of pips that appear on top.

1. What is one outcome of a trial?
2. What is the sample space?
3. What are possible events?
4. What are some disjoint events?
5. What are the probabilities of the events above?

5 mins

05:00

The 3 axioms of probability

1. The probability of the sample space (\(S\)) is 1 (ie \(P(S) = 1\))
2. A probability \(p\) is always between \(0\) and \(1\) (ie \(0 \leq p \leq 1\))
3. If two events \(A\) and \(B\) are disjoint, then \(P(A \cup B) = P(A) + P(B)\)

Your turn

Click here or the qr code below