# Thread: Probability growth with time

1. ## Probability growth with time

Hey, I am not an expert at probability. I've been wondering about a simple question that seem really hard for me to find an answer to simply by googling. There really is no easy way to put my question, so I’m going to just state an example. Say we want to find the probability of a car accident happening in a certain amount of time, how would we go about solving that? I know this would depend on the driver’s skill, places that he drives, etc. But even if we figured all that out, we would still have a problem. Normally a probability is calculated as a possible outcome over a number of possible outcomes. So say the chance of getting a head is ½ because there it is 1 out of 2 possible outcomes, WHEN you toss a coin. But the above question is different, we did not define the WHEN. The when is more like.. a continuous event. I would expect the theory that corresponds to this to be something like a growth curve of possibility that approaches 100% when t->infinity.

EDIT: Please keep it simple, because I don't know a lot about statistics.

2. ## Re: Probability growth with time

One very common modelling, e.g. is to model the time needed for the accident to happen following a certain exponential distribution.

Then in this case the probability that the accident happen in the time interval is the probability that the exponentially distributed accident happening time is less than the length of the interval.

Whenever you have learn some basic of continuous random variable, you should get some rough idea. The "growth curve" you mentioned I guess would be the CDF of a continuous distribution which is a continuous function. And for a continuous distribution, unlike discrete distribution, it has uncountably many support points but has no point mass inside - the probability that the continuous random variable equal to a particular support point is zero.

3. ## Re: Probability growth with time

This is a form of Survival Analysis. In reliability, the growth curve is called a Cumulative Failure Plot. This handbook may help.

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