I've just finished teaching a section in my law school class on quantitative methods in legal decisionmaking. I haven't taught this class for six years, and I had forgotten how remarkably unintuitive but fascinating the study of probability can be.
The class and I have just been discussing the famous Monty Hall problem. Here's one version of it:
Suppose that you have been selected to play the final game on "Let’s Make a Deal" -- the famous television show hosted by Monty Hall. You are offered a choice of whatever lies behind one of three doors on the stage. Behind one of those doors is $60,000 in cash; behind each of the other two is a goat. (The prize has been placed behind one of the doors before the game begins; it will not be moved once the game begins; Monte knows where the prize is placed, but he gets nothing out of preventing you from winning—he’s just a showman and wants the game to be fun.)
You make a selection—say, Door #1. Monty turns to his assistant and instructs him to open one of the two doors you did not choose—say, Door #3. And Voila! There is a goat behind Door #3. Only Door #1 and Door #2 now remain closed.
Monty now turns to you and says, “Before we go any further, let me give you three options. First, you may stick with your initial choice, Door #1. Second, you may switch to Door #2. Or third, I’ll give you $35,000 in cash and you may leave the game right now.” (Assume that you are risk neutral.)
Which option should you take?
I'll post an extended analysis in the next couple of days. Be warned! There is so much more to this problem than meets the eye.
TSU
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