Merry Christmas!

Happy Birthday JC and many more, and a Merry Christmas to all!

Monty Hall Problem

Alright, a little brain teaser for you. First one! Woot!

This is the Monty Hall problem that I came across in the movie 21 and discussing with Jacky when she took a probability class of some sorts before she got owned by strep/mono/chicken pox. Check it. For all I know, you could be the winner of a brand new car, and in your acceptance speech, you'll know who to thank.

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? 

Solution (obtained from mathforum.org):

One way to think about this problem is to consider the sample space, which Monty alters by opening one of the doors that has a goat behind it. In doing so, he effectively removes one of the two losing doors from the sample space.

We will assume that there is a winning door and that the two remaining doors, A and B, both have goats behind them. There are three options:

1. The contestant first chooses the door with the car behind it. She is then shown either door A or door B, which reveals a goat. If she changes her choice of doors, she loses. If she stays with her original choice, she wins.
2. The contestant first chooses door A. She is then shown door B, which has a goat behind it. If she switches to the remaining door, she wins the car. Otherwise, she loses.
3. The contestant first chooses door B. She is then is shown door A, which has a goat behind it. If she switches to the remaining door, she wins the car. Otherwise, she loses.
   

Each of the above three options has a 1/3 probability of occurring, because the contestant is equally likely to begin by choosing any one of the three doors. In two of the above options, the contestant wins the car if she switches doors; in only one of the options does she win if she does not switch doors. When she switches, she wins the car twice (the number of favorable outcomes) out of three possible options (the sample space). Thus the probability of winning the car is 2/3 if she switches doors, which means that she should always switch doors - unless she wants to become a goatherd.

This result of 2/3 may seem counterintuitive to many of us because we may believe that the probability of winning the car should be 1/2 once Monty has shown that the car is not behind door A or door B. Many people reason that since there are two doors left, one of which must conceal the car, the probability of winning must be 1/2. This would mean that switching doors would not make a difference. As we've shown above through the three different options, however, this is not the case.

Vicarious

December 23, 2008. Snowy

Word of the day: Vicarious: adj. Serving instead of someone/something else. Performed or suffered by one person as a substitute or to the benefit/advantage of another.

So 2nd day of class. 6 hours of SSAT/SAT Critical Reading prep. Marathon is more appropriate. I don't know who's more tired, the kids or me. But all I can say is I'm really blessed to have kids who are pretty receptive and hard working, so they make the job all the more easier on my part. All seem pretty motivated or driven, but definitely need some more prep, and I'm hoping I dont fail to deliver. 

Being able to work and provide my family with some income is a really good feeling. I definitely feel a certain sense of accomplishment in knowing that these kids, while I may not necessarily drastically raise their score, at least made an attempt to challenge themselves even though they are exhausted come 4:30. Secondly, while I don't want to view this work as something vicarious for my family's sake that I'll have to miss a semester, I must confess it's been good so far to carry my own weight around the house and see my father's worn face crack a smile for once.

I'll be keeping this up for 2 weeks, and then less hours during the weekdays considering school resumes. God forbid I come down with something these next couple of weeks...

Btw, came acros this in an SSAT book of all places (side note, I never realized how tough the test actually is. For all I know, it's no different than the SAT, and to think, kids in grades 5-7, 8-11, are taking this just for entrance to private or independent schools. I look back at grade 8 when I took it, and wow, if Merriam-Webster decide to define "Epic Fail" my face would appear right next to it.

"Children have an amazing talent for learning vocabulary. Between the ages of one and seventeen, the average person learns the meaning of about 80,000 words - about 14 per day. Dictionaries and traditional classroom vocabulary lessons only account for part of this pectacular knowledge growth. More influential are individuals' reading habits and their interaction with people whose vocabularies are larger than their own. Reading shows students how words are used in sentences. Conversation offers several extra benefits that make vocabulary learning engaging - it supplies visual information, offers frequent repetition of new words, and gives students the chance to ask questions" 

It certainly seems like we underestimate man's own knowledge of this world and beyond. 80,000 words; I'd like to see somebody actually recite them and write that down, but I would have never thought that we could possess such an extensive bank of knowledge dedicated solely to vocabulary alone. Thus it begs the question, what are the bounds to human knowledge? Can there be enough? And how do we know what we really know?

Questions like these I asked myself after taking Epistemology (The Philosophy of Knowledge) this past semester. Granted, the course was arguably the hardest I've taken, and while my grade certainly doesn't reflect my interest in the subject, it definitely got me thinking and forced me to question my own beliefs and understanding of knowledge. And that applies to both physical and spiritual aspects of life. More reflection to come, but this is just to get the ball rolling.

Alright, time to work on a lesson plan for tomorrow. Christmas Eve and Day are so close! If I don't get back to you all, Happy Holidays to all!

~Shimmy

Inauguration

December 22, 2008. Snowy

Word of the day: Impenitent: Adj Not humble, or forgiving. Not feeling regrets for one's sins.

It's been 2 and a 1/2 years in which I've spent time with what I can only call my second home, Columbia. I had been thinking of taking leave for a while now, but never mustered up the courage to do so until things took a turn for the worst for Wall Street and company. And so, with the state of the market which it is in, and the propsects of an economic downturn the likes of which humanity has never witnessed before, here I sit back at home in the ol' T-dot, with the snow falling gracefully on the carpet of grass outside my window, puttings thought onto digital paper. While it seems like the world is crashing and burning before my eyes, to acknowledge this as God's doing is straight up impenitence. And quite frankly to say, while I'll miss my friends (that is, my family!) back home in Columbia, I am elated, and excited by the prospects of what God has in store for this sad creation of His. 

With that being said, I've decided to keep a diary (bloggary if you will) so I don't forget this "detour" on this so-called road of life. Being an SAT instructor, it's funny to go back and realize exactly how many words students attain and retain in their attempts to encounter such words again come test day for that extra point towards a 2400, and so, I'm going to be taking a walk in their shoes, and keep track of any words that I trip over or simply don't know. Hopefully some of these words are profound enough that I'll be abe to write an entire entry around it, utilizing it as a central theme of some sorts. Or most likely, the words are just funny/interesting/story of my life that serve no grand purpose other than maybe improving your vocabulary as well.

Furthermore, I must admit, some of these critical reading passages are pretty money as well, and are surprisingly interesting if taken as leisurely reading devoid of any test taking stress. If you just want a piece of trivia for your day, keep watch!

Finally, as you all know by now, puzzles are a big time killer, and a semester (and summer break, my God) is A LOT of time to kill. So if you too would like to commit (time)icide, feel free to check out any puzzles I share, and watch as you procrastinate and whittle the minutes, hours, (days?) away.

So do these things make my any cooler? Absolutely not. But take what you will, and remember all, I'll brb! Please pray for me as I try to make sense of this time, and that God will continue to serve as my solution manual to my life and provide me with direction and clarity with whatever grand plans He may have.

And now, I rest.

~Shimmy