HCOL 195 9/16/09

I showed everyone my two-headed and two-tailed coins and remarked that they might be a better way to present the RR, RB and BB card experiment.

I asked how people had solved the Monty Hall problem; two people drew trees. I then drew my probability tree, an “natural frequencies” tree (the portion that we needed), and displayed a spreadsheet calculation.

I then attempted, on the spur of the moment, to indicate the spreadsheet calculation for a problem where there are 1,000,000 doors and Monty opens all but two (again, he knows where the prize is, and does not open that door nor the door you chose), revealing 999,998 goats. Unfortunately, since I hadn’t thought of this before and my calculation was spur-of-the-moment, I wasn’t able to complete it. After class I looked at it again and it’s pretty simple; I’ll display it on Friday.

I asked about “Angelic Monty” and “Monty from Hell.” In Angelic Monty, if you pick the right door, Monty opens the door and shows you that you won. If you pick the wrong door, he opens a door with a goat and encourages you to switch (and if you do, you’ll get the prize). Everyone agreed it’s best to switch if you know that Angelic Monty is in charge. On the other hand, Monty from Hell will open the door you picked if you guessed wrong and show you a goat; but if you guessed right, he will open another goat and offer you the chance to switch. In this case, everyone agreed that if you know you have Monty from Hell, you should not switch.

I then mentioned “Mixture Monty.” In Mixture Monty, backstage before the show Monty flips a fair coin. If it’s heads, he behaves like Angelic Monty. If it’s tails, he behaves like Monty from Hell. The question is, if you face Mixture Monty, should you switch, or doesn’t it make any difference? Everyone agreed that it’s 50:50 that the prize is behind your door, so it doesn’t make any difference. I started a spreadsheet with six states of nature, 3 doors for the prize if it’s Angelic Monty, and 3 if it’s Monty from Hell. We put a prior in, and wrote down the likelihood column. However, we were rushed for time, and there was a mistake in that column (and we didn’t finish the calculation). After class, a student found the error. We’ll pick up at that point on Friday.


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