We have to check just two requirements:

(1)   All the probabilities in the P(x)
list must be between 0 and 1 inclusive.

(2)   The sum of the probabilities in
the P(x) list must equal to 1.
----------------------------------
(A)
x    P(x)
1    1/5
2    9/25
3    2/5
4    1/25

It meets the requirements of (1). Let's
check requirement (2) 

Get LCD of 25
 =
 = 1, so yes it is a
probability distribution.
----------------------------------
(B)
x   P(x)
3   0.7
6   1/12
8   0.22
It meets the requirements of (1). Let's
check requirement (2) 


Change the decimals to fractions 
 
Get LCD of 300


 ≠ 1, so NO it is NOT a
probability distribution.
----------------------------------
(C) 
 x    P(x)
20   13/25
30    0.25
40   -0.01
50    6/25

It does NOT meet requirement (1), because of
the negative number in the probability list,
so it is NOT a probability distribution
function.

Edwin