/sci/ - Science & Math

I was watching the 2002 movie Scooby-Doo. There was a scene that (for me) brought up a question about probability. The scene was as follows:

> We have the four main characters on-screen.
> Within the bodies of those characters are four "spirits".
> Of that set of spirits, one belongs to each character, but is not initially within the body of the character it belongs to.
> Randomly, all the spirits will exit the characters, shuffle around and enter a random character such that each character has a spirit within his or her body once the shuffle is complete.

Questions:
> What is the probability that after a shuffle has occured, all the spirits will be in the correct body?
> How many shuffles is it most likely to take before all spirits are within the correct body?