If we indicate with n the number of songs, the probability that a song is replied in k 'trials' is , so that the requested expected value is...
Now I've been thinking about this problem:
Suppose you have 6000 songs on your playlist, each of these songs have an equal probability of being played next (I assume even the song that is currently played).
How many songs are expected to play before the song you're listening to now repeats?
I thought of it in this way:
Let be the event: Current songs replays itself, and be the event that a new song plays.
Obiously, and are independent therefore .
It follows that songs.
Is this approach correct?