What is the distinction between rolling dice and flying in a plane

[cielo]

Intro. I was watching "the day after tomorrow" last night and it was stated something like, "Your odds of dieing in a plane crash are 1 in a billion". A few planes go down in the movie (sorry for the spoiler) and someone says, "So much for 1 in a billion". This got me thinking...For math enthusiasts/experts (i am not one):

We can say a priori (before experience) that the odds of rolling a six on a six sided die is one in six right? Because we know that the likelihood of each side landing up is even (there is nothing we see or suspect of making the 6 come up more or less often).

What about flying in a plane/getting in a car crash etc? We can't measure the odds a priori as with a die. So we establish odds based on #of plane crashes/ # of plane flights, correct? Are these odds, since they are based on empirical data and math, not purely mathematical calculatins, referred to/named differently in probability theory? Are they considered less or slightly less reliable by probability theorists? Are there any sites you know of that discuss this distinction with greater insight? Thanks

cielo

[Piz0wn0reD!!!!!!]

Im not sure but i think the only way to put a number on such events is w/ statistics. I dont think anyone can quantify the odds of a specific car crashing w/o them.

[Lost Wages]

Dice rolling is probability. Plane crashes are statistics.

Link. (http://www.cs.sunysb.edu/~skiena/jaialai/excerpts/node12.html)

Lost Wages

[BigDukeSix]

I don't think its as black and white as that, if you roll the dice enough times, then the stats will equal the probabilty.

If you take the stats of Air travel, you can calculate a probability.

The difference is that probability is the calculation of something and stats are a record.

[blank frank]

Hmm, I just saw The Day After Tomorrow too. Good comedy. /images/graemlins/wink.gif

To get at the distinction you are trying to get at, there is a theoretical construct called a Discrete Uniform Random Variable. We can calculate exactly the probability distribution for this random variable, depending on a parameter n.

When we roll a die, we are assuming that it's distribution is a discrete uniform random variable with n=6. However, the discrete uniform rv only exists in a theotical realm, so there are problems with this assumptions. Usually, the errors involved are so small they are not worth worrying about.

With plane crashes, we can estimate the probability that a given plane will crash based on previous data, with a variety of sophistication ranging from basic to too much. Generally the people who create such estimates understand they are estimates, and qualify their statements with confidence intervals or something. Generally the people who use such statistics don't.

[astrodon]

Except that each roll of the die is mutually exclusive of the previous and there are only six possibilities. Therefore, one can determine within P(A) < .0001 accuracy (actually p = 1) what the outcomes will be and with absolute absence of statistics. Statisics will agree as Central Limit Theorom and the Law of Large Numbers with the probabilities.

However, with airplanes/cars/napalm/atom bombs/hand grenades etc. This is not so. Each event is not necessarilly mutually exclusive and the possibilities are infinite, therefore dependent on some prior[i] (as opposed to a priori) datum.