This is where you are going wrong. the P.D.F isAs I currently understand it, the P.D.F should be the number of times an outcome occurs, divided by the total number of outcomes.justthe probability that the event occurs. Your list approach doesn't work because the different items in the list have different probabilities attached to them.

Lets take f(30) as an example

f(30)=p(10p and 20p) + p(20p and 10p)

=(80/200)*(120/199) + (120/200 * 80/199)

=0.4824

Can you do the rest from here?