I was learning about probability and how does probability works with events and elementary events. So from my understanding, if we throw two dice there are 36 possible results (6 from the one die and 6 from the another), and 2 events that we want to see (1 and 5), so the result should be 2(events that we want to see) / 36 (possible results) = 0.055.
I want to be sure if I'm correct and if I'm wrong please correct me and tell me what is wrong. Thanks for your time!
Formally, we have a probability space $(\Omega, \mathcal F, \mathbb P)$ where $\Omega=\{1,2,3,4,5,6\}^2$ is the sample space, whose elements we call outcomes, $\mathcal F = \mathcal P(\Omega)$ is the $\sigma$-algebra of events (note that $\mathcal F$ can only be defined this way if $\Omega$ is finite or countably infinite), and $\mathbb P$ is a map from $\mathcal F$ to $\mathbb R$ defined by $\mathbb P(E) = \frac{|E|}{|\Omega|}$, where $|\cdot|$ denotes the cardinality of a set. Note that the probability measure can only be defined this way if $\Omega$ is finite, as clearly division by infinity is not well-defined.
Here we are interested in the probability of the event consisting of the outcomes $(1,5)$ and $(5,1)$ - so let $E=\{(1,5),(5,1)\}$. Then $$ \mathbb P(E) = \frac{|E|}{|\Omega|} = \frac 2{36} = \frac1{18}. $$