Tuesday, December 30, 2003 :::
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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, " Do you want to pick door number 2? " Is it to your advantage to switch your choice of doors?
Yes, you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance.
The main question here is whether you should switch, not so much the odds of the prize in the remaining two options. Since the host can ( and will ) open a loser regardless what you have chosen, the chances of the door you have first chosen is still 1/3, since nothing was learned to allow the revising of the chances.
Let's name the doors A, B and C. Suppose the car is always in B.
You chose Door A. The host reveals a goat in Door C. If you switched, you won.
You chose Door B. The host opens either Door A or C, which will reveal a goat. If you switched, you lost.
You chose Door C. The host reveals a goat in Door A. If you switched, you won.
Therefore, the chances of winning if you switched is 2/3. This is the Monty Hall Dilemma.
Think you got it?
Three prisoners on death row are told that one of them has been chosen at random for execution the following morning, but the other two are to be freed. One privately begs the warden to at least tell him the name of one other prisoner who will be freed, and the warden relents. " Susie will go free, " he says. Suddenly horrified, the first prisoner says that because he is now one of the remaining two prisoners at risk, his chances of execution have risen from 1/3 to 1/2!
|
::: posted by Richard Wan at 2:28 PM
Saturday, December 27, 2003 :::
i'm terribly bored. i thought maybe i should just leave the com and read the papers for a good couple of hours or so, but i realised i have already read them. hmph.
gosh. i've started watching simpsons again. and the opening still tickles my fancy.
|
::: posted by Richard Wan at 8:00 PM
At New York's Kennedy airport today, an individual later discovered to be a public school teacher, was arrested trying to board a flight while in possession of a ruler, a protractor, a set square, and a calculator.
Attorney General John Ashcroft believes the man is a member of the notorious Al-gebra movement. He is being charged with carrying weapons of math instruction. Al-gebra is a very fearsome cult, indeed. They desire average solutions by means and extremes, and sometimes go off on a tangent in a search of absolute value. They consist of quite shadowy figures, with names like "x" and "y", and, although they are frequently referred to as "unknowns", we know they really belong to a common denominator and are part of the axis of medieval with coordinates in every country.
As the great Greek philanderer isosceles used to say, there are 3 sides to every angle, and if God had wanted us to have better weapons of math instruction, He would have given us more fingers and toes. Therefore, I'm extremely grateful that our government has given us a sine that it is intent on protracting us from these math-dogs who are so willing to disintegrate us with calculus disregard. These statistic bastards love to inflict plane on every sphere of influence.
Under the circumferences, it's time we differentiated their root, made our point, and drew the line. These weapons of math instruction have the potential to decimal everything in their math on a scalene never before seen unless we become exponents of a Higher Power and begin to factor-in random facts of vertex.
As our Great Leader would say, Read my ellipse. Here is one principle he is certain of---though they continue to multiply, their days are numbered and the hypotenuse will tighten around their necks.
|
::: posted by Richard Wan at 4:18 PM
