Suppose I had an iPod with x number of songs. Suppose one of them is my favourite song. I hit the shuffle button, so a random song plays. If it is not my favourite song, after the song ends, I will move on to the next song in the (shuffled) sequence. If it is my favourite song, after the song ends, I will hit shuffle it again (note that when a playlist is shuffled, each song will be played only once in a random order). This process keeps repeating itself.
What is the average probability per song played that it is my favourite song? Any ideas to the approach of this problem?