Why is this not a valid probability mass function

*Corrected post*

p(x) = 1/6 ( 3 - x ) for x = 0,1,2

I thought this was valid since 3/6 + 2/6 + 1/6 = 6/6 = 1 but the answers say it's wrong. Annoyingly the answers don't say why?

The question also had

p(x) = 1/10 ( 3x - 2 ) for x = 0,1,2,3

I used the reasoning that -2/10 + 1/10 + 4/10 + 7/10 = 1 (similar to above) and this p(x) was indeed valid.

So why is the first one not valid? am I using the wrong method??

Thanks if anyone can explain this!

I agreed with Elizabeth,
The first one is valid PMF and the second is not valid.

PMF have criteria, which all the values of all the function must be non-negative and sum up to 1. The first question is non-negative and sum up to 1, so this probability is valid as PMF. The second question has negative value, which means not valid as PMF.

The answers are transposed. The first one is correct. All probs are
non-negative and add to 1.
In the second case, although they add to one, the first prob is negative,
so not OK.