Puzzle #1

[Dr. Ivory]

Now your number six is still only a one in ten chance of being right and the other door is a [B]NINE in ten chance of being right

Don't think so. The removal of the other eight doors changes the chances of the door you have chosen being the correct one. The chances of that are now 50/50.

Probability is the ratio of favourable outcomes to total outcomes. What the deletion of the other eight doors has done is to change the total number of possible outcomes from 10 to 2. Your choice is still one, but it has gone from 1:10 to 1:2.