Does probability make sense in a contemporary context? see example?

Question

does probability really work out in real life? of course, in a lottery or rolling dice, if you havent rolled a 6, just because your rolled a 1,2,3,4, and 5 on the last 5 tries doesnt make it any more likely to get a 6 on the 6th try since its random supposedly. so how can we really apply this to actual life scenarios,

for instance the probability of the next terrorist attack. now we have a good idea that one is inevitable, but of course that could be wrong, we might never experience another for the rest of our lives, then again thats not really a good bet... but we havent really seen anything since 9/11/01, so with every passing day doesnt the likelihood of a new terrorist attack become more likely? is this even applicable to probability considering the differnt factors at work (ie terrorist fundraising, planning, training, foiled plans by the authorities) that take time and would explain why we havent been unfortunate enough to witness another attack? can someone explain?

so kyle - when people come up with the numbers like 1 in 100000 chance of being hit by a car or something like that, then that would be a misuse of probability?

i mean terrorism as an example in that, sure there are humans perpetrating these acts but to the simple american citizen, it seems like a completely random occurance or action even to the cia fbi, etc

Answer 1

The probability of dice or lotteries is nice and simple to describe. That's why in school you learn about how to work those kinds of probabilities. But the statistical methods introduced there can be extended to work with all kinds of things. Yes, human irrationality and unpredictability can lead to some difficulties in predicting the future, but it is possible.

The term frequently used in statistics for the way the past five rolls of the die don't influence the next one is past-independence, or independence of trials. So with dice, yes, the probability of each roll doesn't depend on any other. With other things, like perhaps terrorist attacks, this may not necessarily be the case. But dependence on the past complicates the issue, so you won't hear too much about that in most probability courses. However, consider the probability that in a given week, someone -- anyone -- will win the local lottery. Then in that case, the probability does indeed increase as more failures (i.e., no one wins) occur, because more people tend to buy tickets as the jackpot increases. Of course, the probability of one single ticket being the winning ticket doesn't increase.

Now consider risk management in businesses and insurance companies. Surely they can't take into account every single source of a loss, and there's no definitive way to put a probability on each one, but through some usually very complicated model, you can approximate the expected loss, and take appropriate measures to counter-act it (such as rate hikes).

One rather interesting point was brought up; if I bet someone, based on a model I've developed, that they were not going whack me with a plastic spork, I'd probably lose. That's because they've been informed of the whole thing. But if I bet you that someone else was not going to hit me with said utensil, I've got a pretty good chance of winning, if you would take the bet. It's sort of like quantum physics: by simply observing your experiment, you change its characteristics. Of course, this probably doesn't come into play too frequently. One possible instance of this could correspond to the terrorist attack idea. If we work out a fantastic model that fits our data tremendously well, and we find that there's practically no possibility of a terrorist attack, and we adjust our defense system accordingly, we suddenly make ourselves an easier target, and thus more likely to be attacked.

One last thing. I would imagine that a model that predicts terrorism would be some massive, complex monster that would have to take into account hundreds of different variables. Even with that, predictions further into the future become increasingly difficult. Basic chaos theory ensures that sort of thing; that's what happens with our weather systems. Even if we manage to get a perfect model, but we round our data to the nearest billionth decimal place, that's enough to throw our calculations off to the point of complete randomness within a few months. (A simple model for this sort of thing is a clock that runs a bit off, say every hour it can measure off 59-61 minutes, randomly chosen in that interval. Then as more time passes, we begin to be completely unsure of how far off it is; in one day, we only know that the actual time is within one hour of what the clock tells us.)

So yes, probability can be used to model contemporary concepts. The only problem is coming up with a good formula to describe the probability distribution. For some things, there may not be one that's simple enough to be very useful, but most things can be approximated decently.

(Sorry to have made this so long, I wanted to make sure I addressed everything decently.)

Answer 2

I think the word "probability" is terribly misused. Everyone always says the "probability of this" and the "probability of that", but the truth is that probability cannot be stretched to certain things - like your example, for instance.

You cannot put a probability on simply a terrorist attack occurring since they are planned and carried out by human beings. It's not like terrorists are sitting in a cave saying "Well there's a 56% chance that I'm going to do this tomorrow. I will use a random number generator to generate a number between 1 and 100 and if the number is less than or equal to 56, I will do it."

In other words, probabilities cannot be made for things that can be manipulated by human behavior. I cannot say there is a 20% chance that I am going to do X tomorrow because I have the ability to decide if I am going to do it. If you bet me that I wasn't going to do X, all I would have to do is DO it. Doing X is completely controlled by me - not by chance.

Hope this all makes sense. The probability that it does is under 1%.


edit:
Good question. You can base the probability of being hit by a car off of statistics from past car accidents, but I still think there is tons of error in a probability like that. Most importantly, human behavior DOES of course contribute to car accidents. I could go out in my car and hit a thousand people today and that would drive up the chances of being hit. So, I believe this is another example of misuse of the word.

By the way, I have seen and answered many questions on here, and I bet many people will overlook this one, but I want to let you know this is one of the best I have seen.

Answer 3

In quality control you use probability every day. You have a machine making some kind of widget that has a dimension that must be held within certain tolerances. You take 25 parts and measure them, then do what's called a 'capability study' to see if the machine is able to get them all within limits, or if you need to use a better machine. Another place probability is used is in insurance. They have people called 'actuaries' who compile statistics to see what the probability is of someone dying in the next year, the next five years, ten years, etc. Someone who smokes is more likely to die. Or someone who takes antidepressant meds, or has a history of heart problems, etc. They figure out how each of these factors affects the person's probabilities, and they figure this into the rates. Big powerful corporations often sell products they know are not as safe as they could be. There was a famous case back in the 1970s with the Ford Pinto. Millions of these cars were sold with a defect that could cause the gas tank to explode if the car was hit from behind. After they found out about it, they did a probability analysis and found that it would be cheaper to just let it happen, and defend themselves against the resulting lawsuits, than to recall all the cars and fix the problem.

Answer 4

I think it's effective if used in the context of "there is less than a 1 in 5 probability that the next role of the die will be a 6. Keep in mind this is not effected by the fact that all the other numbers have been thrown. I do not think it is effective statistics to pin the probability of a terrorist attack down to a real number. The lottery, you can exactly describe the probabilities due to the fact that there is in an infinite number of possibilities, there is a set amount of possibilities derived from how many tickets sold and the chance of getting all six numbers based on past performance.

Answer 5

Probability is applied to many of the things we as humans go through everyday.... you're right especially with lottery and gambling... with the terrorist attacks you have to take other things into perspective... not only look at it as an EVENT. or a bad day in a 365 day calendar year... but in 9/11 we had CIA and FBI that unfortunately knew information and that did not share it between both agencies. If both shared what they knew about Alcaeda and what they knew about Osama and what he had planned then maybe two and two together would see how so Randomly people are taking flight lessons for no appearant reason.

Answer 6

car accidents, slipping in the shower, all those things we have data for and can have empirical data and empirical probabilities. They are subject to so many factors however that it is always wise to take the probabilities with a grain of salt. When it comes to human interaction and systems the models are getting better but not that great. Just look at the weather. the best stochastic models are only good for predicting the weather out to about three days. Some of these calculations take super computers hours to compute. I would say that any one saying we'll be hit by a terrorists with a certain probability has 100% probability of me ignoring them.

Answer 7

I think of probability ultimately as a way of choosing among options. For example, if you have the choice of being given $1, or taking a chance on winning $1000 if a certain event occurs, should you take the $1 or take the gamble for $1000? The probability of the event determines which one to choose. If the probability is less then 1/1000, take the $1. If the probability is greater than 1/1000, take the gamble. If it's exactly 1/1000, choose either one.

Answer 8

Don't overlook small things before you jump to much bigger things like lottery or terrorist attacks. In your routine everyday life you use probability. In fact, there are many instances: crossing the street, calling up somebody on the phone, answering examination questions in school, etc. You did it, do it and will continue to do it but you are just unaware of it.

Answer 9

Reminds me of a Joke, I Heard Long Ago, About Probability, "What is the Probability of Getting On a Jet, With Two Bombs?", Answer: "~1 In 1000000000", Response: "So I Carried a Bomb On a Plane From then On".

Answer 10

well u have 2 types of probability and they are experimental and theoretical and it depend when you have a six sided die your chances of rolling a even number are 3/6. that's a theoretical problem.