Chapter02 Basic Probability

• Sample space: The set of all possible outcome of a certain experiment.
  • i.e. Tossing a coin twice the sample space is $\Omega = \{hh,ht,th,tt\}$
• events: each event is a subset of the sample space.
  • i.e. Let $A$ be the event of getting at least one heads: $A = \{hh,ht,th\}$
• probability measure denote here as as probability function, which indicates the chance of each possible event occuring.
  • i.e. $\mathbb{P}(\cdot)$ takes an event as argument and return a value in the range of $[0,1]$
  • $\mathbb{P}(\emptyset)=0$
  • $\mathbb{P}(\Omega)=1$