probability of getting 2 or 5 in two throws of a die So I know the probability rule of addition. 
Getting 2 or 5 in two throws should be 
$P(2)+ P(5)$.  $P(2) = 1/6, P(5) = 1/6$ so the combined so it should be $1/3$. 
I tried to visualize but not able to do so correctly.
11,12,13,14,15,16, 21,22,23,24,25,26,31,32, ....6,6
total of $36$ possibilities.
12,15,21,22,23,24,25,26,31,35,42,45,51,52,53,54,55,56,61,65
out of which $20$ possibilities, so the probability should be $20/36$ which is not $1/3$.
Where am I going wrong?

I presume that if you know the probability rule for addition, you also know that for multiplication, often called the fundamental counting principle
You need either a 2, or a 5 or both.
In such situations, use of the complement can greatly simplifies computations.
The outcome we don't want, P(neither $2$ nor $5$),
thus $P(2\;or\;5) = 1 - \dfrac46\cdot\dfrac46 = \dfrac{20}{36}= \dfrac59$
