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Quiz 2

2007.04.02 12:00 | links_to_shit_only_we_care_about | db

6 comments

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Quiz 2

I've been following the ongoing email exchange between Harris and Sullivan, during which Harris points to the fallibility of the human mind, and how often intuition can lead us astray. He goes on to cite the "Monty Hall Problem", which I had never heard of. The problem is as follows.

A thoroughly honest game-show host has placed a car behind one of three doors. There is a goat behind each of the other doors. You have no prior knowledge that allows you to distinguish among the doors. "First you point toward a door," he says. "Then I'll open one of the other doors to reveal a goat. After I've shown you the goat, you make your final choice whether to stick with your initial choice of doors, or to switch to the remaining door. You win whatever is behind the door." You begin by pointing to door number 1. The host shows you that door number 3 has a goat.

If you are the contestant, what should you do, and why? Stick with door number 1, or switch to door number 2?

[As usual, the solution can easily be found on the net, so please refrain from looking it up. Answer to follow.]

Comments

I would switch to door number 2 because its not wise to have two goats next to one another, so I assume they would have the car between them.

heather | 2007.03.31 15:56

I say stick with door number one ... seeing door number three doesn't change anything. Besides, goats are cute.

sarah | 2007.03.31 17:20

I would pick door number one.... because even though the guy is honest, I would feel like he was trying to trick me or make me change my mind...

Emily | 2007.04.01 07:46

but what is the probability that the other goat will drive the car out from behind the doors and run Monty over?

gary | 2007.04.01 08:22

With two choices left, one of which is the car and the other the goat, it appears like a 50/50 gamble. However, it turns out that switching your choice to the other door gets you the car 2 out of every 3 chances. This picture illustrates why this non-intuitive answer is correct:

	Host reveals either goat ---->
Player picks car		Switching loses
	Host reveals Goat B ---->
Player picks Goat A		Switching wins
	Host reveals Goat A ---->
Player picks Goat B		Switching wins

The player has an equal chance of initially selecting the car, Goat A, or Goat B. Switching results in a win 2/3 of the time.

db | 2007.04.02 08:03

what?

heather | 2007.04.02 17:39