I woke up a few minutes ago with a new explanation for the Monty Hall problem banging around in my head - demanding an outlet.
I just wish I could find the last time I chimed in on the math behind the problem. It is somewhere on these boards, but I cannot think of the proper search terms to put into Google to find it.
Oh, well. Here's the new explanation why it is always a good idea to switch doors:
There are three doors. You pick one at random, and have a 33.33% chance of getting the correct door.
Assuming you picked the correct one, whichever door Monty does not open must be a wrong door. If you switch, you will lose. This occurs 33.33% of the time.
Assuming you picked the wrong one, whichever door Monty does not open must be the right door. If you switch, you will win. This occurs 66.66% of the time.
Conclusion: Choosing to switch is twice as likely to be the correct choice. You will still occasionally lose, but that's random choice in action. |
