Agenda

Logistics

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• Quiz 1 released Friday, due September 15, 2024 </aside>

Contact: [email protected]

Tutorials → review material + solve problems + answer your questions

Probability Basics

Some definitions to get us started

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Sample Space: a set representing all possible events/outcomes of an action

e.g $\Omega = \{1, 2, 3, 4, 5, 6\}$ for a roll of a single die

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Event: some subset of the sample space $A \subseteq \Omega$, usually consisting of those elements that satisfy some condition e.g $A = \{2, 4, 6\}$, the event consisting of even rolls of a single die

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Probability of an Event (finite, uniform) $^{[1]}$: simply the proportion of elements within an event and the sample space, that is, $P(A) = \frac{|A|}{|\Omega|}$

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$^{[1]}$ when $|\Omega| \in \mathbb{N}$ and each outcome is equally likely (i.e $P(\{t\}) = \frac{1}{|\Omega|}, \forall t \in \Omega$)

• What is $P(\Omega)$, what about $P(\emptyset)$?

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The complement of an Event $A$: denoted $A^c$, the elements of a sample space not in $A$, i.e. $\Omega - A$

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• What is $P(A^c)$?

and some basic laws…

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$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

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• Why do we subtract $P(A \cap B)$??

Question Time 🙂