The Monty Hall Problem

Some months ago, I had the honor of interviewing Monty Hall for a story I was writing. If you don't know, Monty created and hosted one of TV's longest-running game shows, Let's Make a Deal. (non sequitur: I'm once again reminded of that hilarious exchange in Airplane II: Lloyd Bridges's character: "If anyone has any ideas - anything at all - now is the time to speak up." Jacob: "How about a game show like Hollywood Squares, but with kids? Gary Coleman could host.")

So Monty Hall. He was one of those figures I remember from growing up "“ always on TV, someone you could trust to make you smile, an affable host with a pretty interesting game show in his command. The interview went fantastically well, and I learned a lot about not only the origins of the show (the network pulled the plug after seeing the pilot, but later threw it on the schedule as a last-minute replacement for another show that had bombed), but Mr. Hall, too.
mh-1975.jpg What I didn't know when I was a kid growing up watching the show, but only discovered in doing research for the interview, was something known as the "Monty Hall Paradox." (AKA "Monty Hall Problem") In a nutshell, the paradox asks the question: Do the player's chances of getting the car (behind door number 1, 2, or 3) increase by switching doors once a guess has been made (so technically it's down to two doors at that point).

I'll post the answer after the jump, but I'd be interested to know what you think before you click through.

theorum.pngInterestingly, the answer is always YES. From Wiki:

Once the host has opened a door, the car must be behind one of the two remaining doors. The player has no way to know which of these doors is the winning door, leading many people to assume that each door has an equal probability and to conclude that switching does not matter (Mueser and Granberg, 1999). This "equal probability" assumption, while being intuitively seductive, is incorrect. The player's chances of winning the car actually double by switching to the door the host offers.

For a very complex answer to WHY this is so, check out the full Wiki article, including a discussion of Bayes' theorem. If any of you recall my post on Mark Haddon's novel, the curious incident of the dog in the night-time, and have read the novel, you'll also find a pretty cool discussion of the Monty Hall Problem there.

College Board Wants to Erase Thousands of Years From AP World History, and Teachers Aren't Happy

One would be forgiven for thinking that the Ides of March are upon us, because Julius Caesar is being taken out once again—this time from the Advanced Placement World History exam. The College Board in charge of the AP program is planning to remove the Roman leader, and every other historical figure who lived and died prior to 1450, from high school students’ tests, The New York Times reports.

The nonprofit board recently announced that it would revise the test, beginning in 2019, to make it more manageable for teachers and students alike. The current exam covers over 10,000 years of world history, and according to the board, “no other AP course requires such an expanse of content to be covered over a single school year.”

As an alternative, the board suggested that schools offer two separate year-long courses to cover the entirety of world history, including a Pre-AP World History and Geography class focusing on the Ancient Period (before 600 BCE) up through the Postclassical Period (ending around 1450). However, as Politico points out, a pre-course for which the College Board would charge a fee "isn’t likely to be picked up by cash-strapped public schools," and high school students wouldn't be as inclined to take the pre-AP course since there would be no exam or college credit for it.

Many teachers and historians are pushing back against the proposed changes and asking the board to leave the course untouched. Much of the controversy surrounds the 1450 start date and the fact that no pre-colonial history would be tested.

“They couldn’t have picked a more Eurocentric date,” Merry E. Wiesner-Hanks, who previously helped develop AP History exams and courses, told The New York Times. “If you start in 1450, the first thing you’ll talk about in terms of Africa is the slave trade. The first thing you’ll talk about in terms of the Americas is people dying from smallpox and other things. It’s not a start date that encourages looking at the agency and creativity of people outside Europe.”

A group of teachers who attended an AP open forum in Salt Lake City also protested the changes. One Michigan educator, Tyler George, told Politico, “Students need to understand that there was a beautiful, vast, and engaging world before Europeans ‘discovered’ it.”

The board is now reportedly reconsidering its decision and may push the start date of the course back some several hundred years. Their decision will be announced in July.

[h/t The New York Times]

North America: East or West Coast?


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