Finding the PMF of a function of a discrete random variable

The discrete random variable K has the following PMF:



p(k) = { 1/6 if k=0

2/6 if k=1

3/6 if k=2

0 otherwise

}



Let Y = 1/(1+K), find the PMF of Y





My attempt:

So, I am really confused about what this is asking.



I took all of my possible K values {0, 1, 2} and plugged them in to the formula for Y to get:



Y = {1,1/2,1/3}

Then the only Y value that is also a K value is 1 so:



p(y): {1 if y=1

0 ptherwise

}



This does not look right to me.



Am I approaching this the right way?