# Thread: prove pr(E)=0

1. ## prove pr(E)=0

Let U be a well defined universe; S be a well defined sample space. Let E= empty set.

Prove or disprove that Pr(E)=0

2. In the axioms of probability there are at most three axioms.
If $S$ is the space then $P(S)=1$.
If $A\cap B=\emptyset$ then $P(A\cup B)=P(A)+P(B)$.
Using those two it is easy to show that $P(\emptyset)=0$

3. note that probability zero doesn't mean the set is empty
For example, the cubs have zero chance of ever winning a world series
and yet they may in 10,000 years