Here is how it's going to be this month: Monday (or today, whatever) I'll post a puzzle I have from a book on Monte Carlo problems. A Monte Carlo method (or simulation, or experiment) is a "broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; typically one runs simulations many times over in order to obtain the distribution of an unknown probabilistic entity." This early in the morning I'm having trouble with definitions, but it's steps that a computer (or person, really) takes with random numbers in order to solve problems with random numbers. They are fairly easy to build. There are articles on how to run them in Excel or any similar spreadsheet program. Like I said, if you have the right random number generator, like a standard die or maybe some multi-sided dice, a person could do the simulation with paper and pencil. It just might be tedious.
Okay, so here is the problem, taken from the book "Digital Dice: Computational Solutions to Practical Probability Problems". I left my copy. . . somewhere. . . so this is the easy intro problem:
- A clueless student faced a pop quiz: a list of 24 presidents of the 19th century and another list of their terms in office, but scrambled. The object was to match the president with the term. He had to guess every time. On average, how many did he guess correctly?
- Imagine this scenario occurs 1000 times. On average, how many matches (of the 24 possible) would a student guess correctly?