I have been given 4 keys of the four different offices with the instructions that one of these keys will open your office door lock. Unfortunately, all the keys look identical so to open the office door I have to try them at random.

I will need to open my office door under the following alternative assumptions.

(a)After an unsuccessful try I mark the corresponding key so that I never tryit again, and

(b)At each trial I am equally likely to choose a random key.

What will be the Probability Mass Function (PMF) using both the above assumptions?