Number of possible events is $2^N$ ( $N$ is the number of outcomes )? A probability space is a random process or experiment with
three components:
–
$Ω,$ the set of possible outcomes $O$
*number of possible outcomes = $|Ω| = N$
*$F$, the set of possible events $E$
      - an event comprises $0$ to
$N$ outcomes


*

*number of possible events
= $| F | = 2^N$ 


Here I am not able to extract the exact meaning of number of possible outcomes. In case of tossing a coin, we have only $2$ outcomes. So, $N = 2$. So, either we have head or tail. According to the above definition, $|F| = 2^N = 2^2 = 4.$ How come this formula or axiom is valid in probability space ?

The answer by drhabs is wrong, his answer misses the null set. 2^n comes from the fact that for each element in your set you have 2 choices, to either include or not include it in a subset. For the example Ω={H,T} you will have the following subsets:


*

*{H,T} (every set is a subset of it's self)

*{H} 

*{T} 

*{} (null set)

