# how to do i prove this simple probabilty result

I want to prove that $P(|A+B|>c)\leq P(|A|>c/2)+P(|B|>c/2)$, where $A$ and $B$ are random variables and $c>0$.

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Hint: Use the following: If $|A|\leq c/2$ and $|B|\leq c/2$, then $|A+B|\leq c$. It might be useful to negate this statement and then use the subadditivity of the probability measure.