Probability Distribution Function

Hello everyone, Ive encountered a problem during revision with the following question:

A money Box contains 80x10p and 120x20p coins. Two coins are taken out at random without replacement. Calculate the Probability Density Function (P.D.F), f(x), where x is the total monetary value of the coins taken out.

I originally tackled the problem by writing down all the possible outcomes:

10p + 10p = 20p

10p + 20p = 30p

20p + 10p = 30p

20p + 20p = 40p

As I currently understand it, the P.D.F should be the number of times an outcome occurs, divided by the total number of outcomes. So I worked out the P.D.F as:

f(20p) = 1/4,

f(30p) = 2/4,

f(40p) = 1/4.

However, according to the answers this is wrong. Can someone please explain where Ive gone wrong?

According to the answer booklet, the P.D.F should be:

f(20) = 0.1588

f(30) = 0.4824

f(40) = 0.3588

Any Help would be very much appreciated!

Alex