The answer to yesterday’s puzzle: If you want another perspective on the problem then wander over to NotSoSoft where Meg has explained it all. Other people also got the answer correct, but weren’t nearly as forthcoming about the process. Here’s my solution for you all:
Here are the three doors:
—1— —2— —3—
Behind one of the doors is the thing we want. Behind the other two are things we don’t want. We select a door, but before it is opened, another door is opened to reveal a thing we don’t want and we are offered the choice to switch from our original choice to the other door.
Let’s assume that we chose door one, as it doesn’t make much difference which one we select. Here are the potential variations:
—1— —2— —3—
GOOD BAD BAD
—1— —2— —3—
BAD GOOD BAD
—1— —2— —3—
BAD BAD GOOD
At this stage then, we have a one in three chance of being correct. At this point one of doors two or three is opened to reveal a BAD thing. The
doors that CAN be opened to reveal a bad thing are bold below (don’t forget we have selected door one so that can’t be opened):
—1— —2— —3—
GOOD BAD BAD
—1— —2— —3—
BAD GOOD BAD
—1— —2— —3—
BAD BAD GOOD
If you STICK in the first variation you will definitely win, but in either
of the other two you will definitely lose. If you SWITCH, in the first variation you will definitely *lose*. In the
second and third variations you will definitely win. Which means the chances of you winning if you STICK remain 1/3, but the
chances of winning if you SWITCH are 2/3. Therefore you should switch.