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# True or False: Two independent events are always mutually exclusive.

Toolbox:
• If $p(A\cap B)=p(A)p(B)$  for independent event
• Two events $A$ and $B$ are independent. Simultaneous occurance of $A$  and $B$ given by $p(A\cap B)=p(A)p(B)$
But by defination of mutually exculusive events if $A$ occurs and  $B$ does not occurm .$\Rightarrow p(A)>0\Rightarrow p(B)=0$ .$A$  and $B$ do not occur simultaneously and if $B$ occures $p(A)=0$
The given statement is 'False'.

edited Jun 18, 2013