# 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 $P(A \cup B) = P(A) + P(B)$