#Probability Problems

The Orderly Pursuit of Pure Disorder.

Discover, January, 1981

American Heritage Dictionary defines Probability Theory as the branch of Mathematics that studies the likelihood of occurrence of random events in order to predict the behavior of defined systems. (Of course What Is Random? is a question that is not all that simple to answer.)

Starting with this definition, it would (probably :-) be right to conclude that the Probability Theory. being a branch of Mathematics, is an exact, deductive science that studies uncertain quantities related to random events. This might seem to be a strange marriage of mathematical certainty and uncertainty of randomness. On a second thought, though, most people will agree that a newly conceived baby has a 50-50 chance (exact but, likely, inaccurate estimate) to be, for example, a girl or a boy, for that matter.

Interestingly, a recent book by Marilyn vos Savant dealing with people's perception of probability and statistics is titled The Power of Logical Thinking . My first problems will be drawn from this book.

As with other mathematical problems, it's often helpful to experiment with a problem in order to gain an insight as to what the correct answer might be. By necessity, probabilistic experiments require computer simulation of random events. It must sound as an oxymoron - a computer (i.e. deterministic device) producing random events - numbers, in our case, to be exact. See, if you can convince yourself that your computer can credibly handle this task also. A knowledgeable reader would, probably, note that this is a program (albeit deterministic) and not the computer that does the random number simulation. That's right. It's me and not your computer to blame if the simulation below does not exactly produce random numbers.

When you press the "Start" button below, the program will start random selection. Every second it will pick up one of the three numbers - 1, 2, or 3. You can terminate the process anytime by pressing the "Stop" button. Frequencies of selections appear in the corresponding input boxes. Do they look random?