Bert: Hey Art, this is great music!
Art: Thanks! I compiled the play list myself, and wrote my own app to play it.
Chaz: I noticed that all the songs are exactly 4 minutes long, pretty cool!
Bert: Is the song selection random?
Art: Yes, perfectly random using the full list each time a song is selected.
Chaz: I guessed that – there have been a few repeats.
Art:, True, but not too many – there are enough songs to last 8 hours.
Bert: Good, I’d like to hear my favorite song again before we stop!
Assuming that the app has just been started:
1) How many songs will Bert have heard before there is a better than 50/50 chance he will hear his favorite song?
2) How long on average would Bert have to wait to hear his favorite song twice?
3) How many songs would have to be in the playlist so that it is greater than a 50/50 chance Bert will NOT hear his favorite song in 4 hours?
4) BONUS: Art rewrites his app such that songs already played have a 50% reduced chance of being selected again vs. an unplayed song (until the full list is played). Answer questions 2-3 again.
