How about a book test?
You hold up an envelope which you say has a prediction inside. Have the CD player on the table along with three books, have a volunteer choose one of the books, ask them to flip through and allow the pages to fall open naturally at any point, then have then read from the top of the page.
The prediction is opened to reveal the words 'Play me' written in bold font, the volunteer plays the C.D. and it's an audio book at the same point as the spectators choice, you can then take the C.D out to show it's the same book as the one selected, and written on the C.D. or in the C.D case is the page number stopped at.
If you can get a C.D. player with a small remote and you can make / edit your own C.D., you could get more scope as to what page they stop on or even what point in the book they start reading.
However I do think a stronger ending to a show would be a popular song 'fairly selected' from a list by the entire audience and played, but you'll have to work on proving that all the song options aren't on the C.D.
Actually if you can hook the C.D. player up to a computer (or keep it simple, just have the computer speaker hidden behind the C.D. player) than you can have someone name literally any song and just have a friend backstage get the song up on youtube.
If you have the money and you want to disprove a 'high tech' solution you can buy a simple or antique
Record Player and a
Blank Vinyl
Invoke not reason. In the end it is too small a deity.