hi,
can anyone show me why is this true:
$\displaystyle P(\cap_{i=1}^{n}E_{i}) \leq P(\cup_{i=1}^{n}E_{i})$
P is a probability function
thank you
Do you understand the definitions of "$\displaystyle \cap$" and "$\displaystyle \cup$"? $\displaystyle x\in A\cap B$ if and only if x is in both A and B. $\displaystyle x\in A\cup B$ if x is in either A or B.
If $\displaystyle x\in \cap E$, then x is in every set in E. So certainly, $\displaystyle x\in \cup E$.