I saw a question some hour ago which sadly got closed because it was duplicate so I did not have the time to figure out an answer.
Can we use Markov chains to calculate the probability that if having 7 concerts during one week and every concert is equally probable to happen any day, what is the probability that they all end up on all the 7 different days?
Something along the lines of:
- Select one day for the first concert. This succeeds in 100% of the cases, because every day is free.
- Select one day for second concert. (Given that 1 succeeded), this succeeds with rate 6/7, since there is only one day which yet is taken.
- Select one day for third concert. (Given that 2 succeeded), this succeeds with rate 5/7, since there are only two out of seven days which are yet taken.
- ...
So every success above takes us to one new state and every failure takes us to some failure state which we can't get out of.
Is this a valid approach to solve this problem or am I missing something?