Function cannot be used as p.m.f I have the following question:
Give one reason why the following function cannot be a probability mass function:
$$ p(x)= \frac{1}{10} (x+2)$$ where $x=1,2,3$
The solution that i have, but i'm not sure if its an answer, is that if I sum all possible outcomes, they are different than $1$. 

You do need the total probability for all $x$ to sum to $1$, but in this case the sum of the probabilities of all possible outcomes is greater than $1$, not less than.
That is, $3/10 + 4/10 + 5/10 = 12/10 > 1$.
So the core reason is right (i.e., sum must be $1$) but your arithmetic looks to be a bit off.
