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


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