Pop Goes the Economy

So I got this idea a few years ago, when my old math teacher and I went kayaking in DC.  We would talk about anything, from stupid 80's movies, to strange mathematical concepts, and a lot in between.  Anyway, the point is, one day we mentioned collecting quarters.  She explained that she collected quarters, as did I, and 50 cent coins. This is where it gets interesting: we started thinking about just how many people collected the 50 state quarters.  That's gotta be a lot of people, and in turn, a lot of quarters.  And all those quarters are out of circulation, but they exist, with the potential to be put back in.  So what if, one day, all of them WERE put back in? What would happen?  Would anything happen?  Let's say, that by some miracle, out of the 300,000,000 people in this country, 100,000,000 seriously collect enough quarters to have the 50 states.  That's 50 quarters a person.  So, 50 quarters times 25 cents equals $12.50.  $12.50 times 100,000,000 is $1,250,000,000.   1.25 billion.  Sounds like a lot, but in the scale of the economy, its not too much.  But what about even more SERIOUS collectors, the people who have collected the 50 states over... 3 times.  That's 150 instead.  To make things even MORE complicated, just think about how many REPEATS the first 100,000,000 people had.  They must have had 20 or 30 repeats each.  Let's say 20.  So those original 100,000,000 now have: [20 (repeats) + 50 (states) ] * .25 (dollars per quarter) *100,000,000 (people) = $1,750,000,000.
THEN we have to add on the serious collectors.  Lets say they have every state 3 times over, and 20 additional repeats apiece, like the others.  [20 (repeats) + 50 (states) ]* 3 (full sets) * .25 (dollars per quarter) *10,000,000 (people)= $52.50* 10,000,000= $525,000,000.  Now add that on to the earlier 1.75 billion dollars, and we get 1.75 billion plus 0.525 billion= $2.275 billion or $2,275,000,000.  Now if all that got pumped back into the economy, in one night, it might cause something.  If in one moment suddenly over 2 billion dollars got put into circulation, it might cause a slight dip in the economy, due to the value of the dollar decreasing due to over abundance of in circulation money.
Who knows though, what if someday, everyone in the USA has 50 state quarters, repeats and all, and dumps THAT back in.  It'd be fun to watch thats what.

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.