All the probabilities must be

1. All probabilities between 0 and 1 inclusive.  
2. The sum of all the probabilities must
equal exactly 1

(A)  
 x    P(x)
 1    1/4
 2    5/12
 3    1/3
 4    1/6
 
1.  All those probabilities are between 0 and 1.
2.  The sum of the probabilities is
    +++=
    Get an LCD of 12:
    +++=
     =  = 
    No, that sum is not 1, so it is NOT a
    probability distribution  

(B) 
 x   P(x)
 3    0.1
 6    3/5
 8    0.3
 
1. All those probabilities are between 0 and 1.
2. The sum of the probabilities is
   0.1++0.3 = 0.1+0.6+0.3 = 1.0
   Yes, that sum is 1, so it IS a probability
   distribution. 

(C) 
 x   P(x)
20    0.2
30   -0.2
40    0.7
50    0.3

 1.  That second probability is negative, and
     so it is not a probability distribution.   
 2.  The sum of the probabilities is 1, but
     that does not matter. No probability is
     ever negative.  So it is NOT a probability
     distribution.

Edwin