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# True or False: If A and B are independent,then $P(exactly\; one\; of \;A,B\; occurs)=P(A)P(B)+P(B)P(A)$

Toolbox:
• If $A$ and $B$ are independent events associated with an experiment.
• $P(A\cap B)=P(A) P(B)$
• Also if $A$ and $B$ are independent $\bar{A}$ and B are independent and $A$ and $\bar{B}$ are independent and $\bar{A}$ and $\bar{B}$ are indepenmdent.
P(exactly one of A,B occurs)
$=P((A\cap \bar{B})+P(\bar{A}\cap B))$
$=P(A\cap\bar{B})+P(\bar{A}\cap B)$
=$P(A)P(B')+P(A')P(B)$
The given statement is True

+1 vote