Probability Problem

filmismymedium

filmismymedium

Well-known member
I had an argument with my friend about this:

A Person chooses to do a certain illegal action. They do this action every day. Each time that they get away with this act, their chances of getting caught for this act increase. (correct?) This is because every time they choose to do this act, they are taking away from the total pool (which is the total amount of days they decide to do this stupid act).

For instance: A man decides to run a stop sign every day of his life. Each day that he does not receive a ticket, his chances of getting a ticket the following day increase, because he has one less day alive.


Am i right here??????????????????
 
no.

theres a 50/50 chance of landing on heads when flipping a coin with 2 sides (heads and tails, just so theres NO confusion)

Now, if i flip a coin 100 times, and all 100 times it lands on Heads; what are the chances of landing on heads on the 101st flip ?

the same as it is the first time i flipped the coin, 50%.


Other factors come into play but when simplified down like you are doing, do you know this total pool of how many times you can do something? there isnt. theres things like people catching on and what not, but your logic on probability is incorrect.
 
its late, but upon re reading your post, i also believe, that one , if they wanted, could argue...

with less days left in life in this stop sign scenario, he will have a smaller chance of getting caught because he will be commiting the crime one less time than before. :/

in any case , g'night
 
yes but your example assumes that you can continue flipping that coin unlimited times. Here we are talking about day to day. And we definitely do not have unlimited days alive.

Wouldn't our denominator decrease?

Say a deck of cards represents our lifespan (i.e. 52 days for this purpose) and we have a 50% chance of getting an black or red card. If we took out a lot of one color of card, our chances of getting the other card would increase yes?
 
Cynic821 said:
its late, but upon re reading your post, i also believe, that one , if they wanted, could argue...

with less days left in life in this stop sign scenario, he will have a smaller chance of getting caught because he will be commiting the crime one less time than before. :/

in any case , g'night
Click to expand...


haha, yea its late. and you beat me to it. so what do other people think?
 
im back,

The card theory doesnt necessarily agree with the stop sign situation. Because with the stop sign, there is a possibility that he will NOT get a ticket. If on his last day of life, he runs the stop sign, he is not garunteed to get a ticket, its probably the same chance as when he decided to do it the first day. Right?

With the cards , we know for a fact that there are red cards, and we will be forced to pick them. There arent a number of tickets that he must recieve and we just dont know what day he will get them. There are no gaurnteed tickets for runing the stop sign. One is an absolute the other is a day to day or each time by each time. like flipping a coin.
 
I have to agree with Cynic on this one. It is a 50/50 chance reoccurring daily, either he gets busted or he doesn't. Therefore he is just as likely to get caught the first time he commits the act as he would the very last time he commits the act. he is also just as likely every day to not get caught. Like Cynic said, there is no guarantee that he will ever get caught. . . Unless of course you want to start factoring in old age, the progression of technology that the cops use etc. but I don't think that is what this question is about.

So what is it that you do illeagally every day ? :)
 
The only other factor to consider is that if these are individual actions from day-to-day, then they stand on their own with the same percentage of probability (i.e. the coin will always have a 50% chance of coming up heads on each individual flip). But, if your friend says from Day One, I am going to run the stop sign everyday for a week, then his chances of getting caught increase over time, depending on how many days he plans to run the sign. With the coin example, it would be like saying, "I'm going to flip this coin 10 times, what are the chances of getting heads?" The more flips, the more of a chance.
 
Ah, Scharky, ya beat me to it. Looking at our posting times, I was writing while you were posting!
 
Hmm, I think the OP may actually be right, as each day would be defined as the number of "Trials" but the trials are n- 1 for each passing day.

The probability is P(x) of getting caught is, something something, I'm too tired to explain, but I will probaly confirm it later, need to look back at my maths notes on this one.

It may end up how you define each trial wether its mutually exclusive etc..

Too tired..
 
You would probably enjoy Taleb's new book, "The Black Swan". There you will learn that on the day he's caught, not only will there be a cop, but a little old lady in a Honda Civic will T-bone his car and he'll get charged with manslaughter.
 
The deck of cards is not a correct analogy because it requires using "conditional probability", i.e. future events are determined by a past event. Unless something in the stop sign scenario is changed by running the stop sign, then the probability is always the same (whatever it is).

Now, the real world a neighbor may complain to authorities about excessive stop sign running, and there you have affected future outcomes.
 
What about the other complex factors such as, availabe police per square area at any moment at any given location, police patrol routes WRT time and geographical location.

You can start to see that modelling this can quickly get complex. Start off with simple assumptions and build your solution progressive after each successive iteration of the mathematical model.
 
filmismymedium said:
I had an argument with my friend about this:

A Person chooses to do a certain illegal action. They do this action every day. Each time that they get away with this act, their chances of getting caught for this act increase. (correct?) This is because every time they choose to do this act, they are taking away from the total pool (which is the total amount of days they decide to do this stupid act).

For instance: A man decides to run a stop sign every day of his life. Each day that he does not receive a ticket, his chances of getting a ticket the following day increase, because he has one less day alive.


Am i right here??????????????????
Click to expand...

it's possible that as his skill improves, his chances of getting caught are less.
 
It is also possible that the county decides to implement Smart CCTV (ala London style) thus making the whole argument a mute point.

These Damn smart Cams automatically read your number plates and lookup the national database, they know who you are, where you live everything, and if your speeding, jumping lights, in the bus lane etc.

You get an automated digital photo letter and fine through your post. Even if you decide to hide your number plate, the cameras are sharp enough to the shot of the drivers head.

Now if you decide to drive around with a balaclava and no number plates, well I think THAT would raise the probability that you will be spending the night with greasy "Bob" your 250 lb cell mate (who hears voices in his head).
 
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