The Car and Donkeys

A TV show contest problem:

You participate in a TV show, where you are shown three huge boxes. One of the boxes contains a car, and two of them contain a donkey. If you manage to pick a box which has a car, you win it; if you pick a donkey, you lose.

The show routine is this:

You select one of the boxes.
The show host opens one of the remaining two boxes and shows that there is a donkey inside. The car is either in the remaining box or in the one you picked.
Now you have a chance to change and select the remaining box

The problem: should you change selection?

What are the probabilities of winning the car if you change, or if you do not change?

This is a variation of what is know as the Monty Hall Problem in rec.puzzles. (I learnt that after publishing this page).

Think it over!

Then check the answer here.

Published in Njet Problem! collection 1996-01-22.