Add up all the probabilities and see if they are all positive,
between 0 and 1 and have a sum of EXACTLY 1.

A)
   x |  1    2   3   4
 ------------------------
 P(x)| 3/16 3/8 1/4 3/16

Ther are all positive between 0 and 1.  Let's add them:



They have sum exactly 1, so this is a discrete probability distribution.


 
B) 
   x |   3    6     8
 ----------------------
 P(x)| 0.11 21/25 0.06

They are all positive between 0 and 1.  Let's add them:
 


Those probabilities do not have sum exactly 1, so it is not a probability disturibution.


C) 
   x |   20   30  40   50
 -----------------------------
 P(x)| 11/20 0.15 1/5 0.1

They are all positive between 0 and 1.  Let's add them: 


11/20 +0.15 +1/5+ 0.1 = 11/20 + 15/100 +1/5 +1/10 = 55/100+15/100+20/10010/100 = 100/100 = 1}}}

They have sum exactly 1, so this is a discrete probability distribution.

Edwin