<s>[INST] What is the probability of getting a sum of 7 or at least one 5 when you roll two die Please tell me how to approach this problem.
(Sum of 7) = {4+3, 3+4, 6+1, 1+6, 5+2, 2+5} = 6
 (At Least one 5) = {1+5, 2+5, 3+5, 4+5, 6+5, 5+1, 5+3, 5+4, 5+5, 5+6} = 10  
so the answer will be 16/36 = 4/9 ?  
 [/INST] You double counted some possibilities (the two events are not mutually exclusive!). By taking the union of the sets of desirable outcomes, we obtain:
$$ \left\{\begin{align*}
&(1,5),(2,5),(3,5),(4,5),(5,5),(6,5),\\
&(5,1),(5,2),(5,3),(5,4),~~~~~~~~~~~(5,6),\\
&(1,6),(6,1),(3,4),(4,3)~~~~~~~~~~~~~~~~~~~~~~~
\end{align*}\right\}$$
so the probability is:
$$
\dfrac{15}{36}=\dfrac{5}{12}
$$
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