probability space

a probability space consists of a sample space $\text{[math]}$ and a broken link: blk:1711189957 $\text{[math]}$ which takes an event $\text{[math]}$ as input and returns $\text{[math]}$ , a real number between 0 and 1, as output. the function $\text{[math]}$ must satisfy the following axioms:

$\text{[math]}$ .
if $\text{[math]}$ are disjoint events, then $\text{[math]}$

[cite:@blitzstein_probability_2014]

some stuff from college

a probability space $\text{[math]}$ is a mathematical construct that provides a formal model of a random process or "experiment".
a probability space consists of three elements:

a sample space, $\text{[math]}$ , which is the set of all possible outcomes
an event space, which is a set of events $\text{[math]}$ , an event being a set of outcomes in the sample space
a probability function, $\text{[math]}$ , which assigns each event in the event space a probability

rolling 2 dice cubes:
$\text{[math]}$

$\text{[math]}$