Monty Hall Dilemma - Winning a GTI on a Game Show

[cme2c]

WOW 7 days and 10 pages

I'd just like to add that 4 out of every 3 people don't understand statistics.

And most people have more than the average number of feet.

[Mr.B]

66.6%

http://www.stat.sc.edu/~west/javahtm...MakeaDeal.html

As a motivating example behind the discussion of probability, an applet has been developed which allows students to investigate the Let's Make a Deal Paradox. This paradox is related to a popular television show in the 1970's. In the show, a contestant was given a choice of three doors of which one contained a prize. The other two doors contained gag gifts like a chicken or a donkey. After the contestant chose an initial door, the host of the show then revealed an empty door among the two unchosen doors, and asks the contestant if he or she would like to switch to the other unchosen door. The question is should the contestant switch. Do the odds of winning increase by switching to the remaining door?

The intuition of most students tells them that each of the doors, the chosen door and the unchosen door, are equally likely to contain the prize so that there is a 50-50 chance of winning with either selection. This, however, is not the case. The probability of winning by using the switching technique is 2/3 while the odds of winning by not switching is 1/3. The easiest way to explain this to students is as follows. The probability of picking the wrong door in the initial stage of the game is 2/3. If the contestant picks the wrong door initially, the host must reveal the remaining empty door in the second stage of the game. Thus, if the contestant switches after picking the wrong door initially, the contestant will win the prize. The probability of winning by switching then reduces to the probability of picking the wrong door in the initial stage which is clearly 2/3.

Despite a very clear explanation of this paradox, most students have a difficulty understanding the problem. It is very difficult to conquer the strong intuition which most students have in this case. As a challenge to students who don't believe the explanation, an instructor may ask the students to actually play the game a number of times by switching and by not switching and to keep track of the relative frequency of wins with each strategy. An applet has developed which allows students to repeatedly play the game and keep track of the results.

[gareth_oau]

well its good to see I'm capable of appreciating and achieving counter-intuition!

[Buller_Scott]

timbo, yes i have read the question wrong my fair share of times- heck, i even did it this time when i failed to acknowledge the role of the host and his function as intentionally revealing a certain failure first time round.

i've been asked to go home and try it with a deck of cards. okay- i will. one thousand times. 99% of which, i will only bother to deal with two cards. meh- i think it's a case of either we grab some table water crackers, some brie and some olives and a nice bottle of wine, all meet up somewhere and have a lovely monty hall dilemma discussion/picnic, or we all agree to disagree.

it's abit of a shame that this thing is coming to an end. im going to miss it.

[Timbo]

....sounds like a plan!

You could always use Mr.B's simulator, but who trusts computers with these types of game??!! I have bridge and chess games, and I'm convinced the computer cheats

[Timbo]

Maybe in your universe buddy!

50:50 is the right answer

I take it the cat was a little bit pregnant, too

[team_v]

I take it the cat was a little bit pregnant, too

Jeez, if the cat was pregnant that just adds a whole other level of complexity.

You might as well just divide by 0.

[Spilledprawn]

This is awesome

[Timbo]

You might as well just divide by 0.

Make it a number approaching 0, and it's game on

[team_v]

Make it a number approaching 0, and it's game on

The number is inifniti, just to screw with you