You are allowed to take a certain test three times, and your final score will be the maximum of the test scores. Your score in test i, where i = 1, 2, 3, takes one of the values from i to 23 with equal probability 1/(24-i), independently of the scores in other tests. What is the PMF of the final score?

What is the probability that your final score is 16?

What is the probability that your final score is 21?