Solution to 6):

The candidate should choose gate C. To see why, consider a hundred gates. The candidate chooses one, and the host opens 98 others, leaving the one the candidate chose and another one unopened. It should be obvious that the prize is more likely to be behind the gate the candidate has not chosen, since the host will open all gates except for the one the candidate has chosen and the one behind which the prize is (or otherwise the game could not be continued).