TPC Probability Blog Post

I decided to go on a bit of a tangent (ha) for my blog.  We've been discussing probability and dependent/independent events.  I want to write about The Monty Hall Problem, also known as the Game Show Problem.  The idea is this: You are given the choice of three doors, behind one is a car and behind two are goats.  You choose Door 1, the host opens up door 3, to reveal goat.  At this point he asks you if you'd like to switch choice of door or stay with his current choice.  The big question is, is it in your favor to switch or not?

For a lot of people, the answer is: Doesn't matter.  When there are only two doors left, you have a 50/50 chance of getting the car, so switching will do you no good.  In fact, some people even claim it's better to now switch, because even with a 50/50, the host is trying to trick you into choosing the wrong door by switching.  They're trying to use reverse psychology. The flaw in that thinking goes back to the base of the problem though, in that it's not a 50/50.  Its a 2/3 to 1/3 chance if you switch. The idea is that once one door has been opened, you can choose to switch, and now you have the 1/3 chance of your new door, as well as being able to discount the 1/3 from the door opened to reveal a goat.  Leaving only 1/3, to be added to potential successes.  If this sounds weird, and I know it does, Im including a link to a diagram that may help.  Please look at it, it helps a lot, and it looks a lot like the tables we're working with right now.

https://www.google.com/search?q=monty+hall%3B%3B+problem+diagram&safe=off&es_sm=91&biw=1280&bih=664&source=lnms&tbm=isch&sa=X&ei=13L2VJz3DNWmyAT__oCgCw&ved=0CAYQ_AUoAQ&dpr=0.9#imgdii=hKfYzkMgRnZYPM%3A%3BlDjQkxxSg4LaeM%3BhKfYzkMgRnZYPM%3A&imgrc=hKfYzkMgRnZYPM%253A%3BTfLPnLkFrv2UlM%3Bhttp%253A%252F%252Fwww.ashford.zone%252Fimages%252F2008%252F03%252Fthemontyhall.jpg%3Bhttp%253A%252F%252Fwww.ashford.zone%252F2008%252F03%252Fthe-monty-hall%3B500%3B452

In reality, it is a 2/3 to 1/3 chance of success if you take the door switch.  This also shows that the choice of doors are not independent of one other.  I include that just to tie it in a bit more to our current lesson.