Let be the sample space and A be an event.

Question

Let $\Omega$ be the sample space and $A\subseteq\Omega$ be an event. Statements: (S1) If $P(A)=0$, then $A=\varnothing$. (S2) If $P(A)=1$, then $A=\Omega$. Then

Accepted Answer

Consider $\Omega=[0,1]$ and $A=\{1/2\}$ (a single point with continuous uniform measure). Then $P(A)=0$ but $A
e\varnothing$, and $P(\Omega\setminus A)=1$ while $\Omega\setminus A
e\Omega$. So both statements are false.

Solutions · 1