Question about implication and probablity Let $A, B$ be two event. My question is as follows:
Will the following relation holds:
$$A \to B \Rightarrow \Pr(A) \le\Pr(B) $$
And why?

Yes. Since events are sets of states, $A\implies B$ means $A\subseteq B$, which is equivalent to $B=A\cup(B\backslash A)$, a disjoint union. So $P(B)=P(A)+P(B\backslash A)\geq P(A)$. 
