Probability growth with time

elite5chris

I've been wondering about a simple question that I can't just google and get the answer to. Usually when we calculate probability, we know the number of possible outcomes. Say we toss a coin, there are 2 possible outcomes with one being head and one being tail. So the chance of getting a head is 1/2, WHEN you toss the coin. So maybe "tossing the coin" is a defined event. What if the event is continuous in time? What if say, instead of tossing the coin, I balance the coin so it rolls down the hills, and I ask the question, what is the chance of the coin losing its balance after rolling down the hills for 10 seconds, for 20 seconds, and so on? A more practical example would be what is the chance of getting into a car accident after driving for x amount of time? I would expect the theory that corresponds to this to be a growth of probability with respect to time where it reaches 100% when t->infinity.

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micromass

I'm not sure what your question actually is. But events like the one you posted in the OP can be handled with continuous distributions (and even with discrete distributions). For example, check the exponential distribution: http://en.wikipedia.org/wiki/Exponential_distribution

Stephen Tashi

Taking the viewpoint of conditional probability, the usual way to look at things is that "The probability of event A given event B" does not change with time. If you want time to enter the picture you define a function that maps time to events. So "The probability of A given B(t)" can change with time because as time t changes, the event B(t) becomes a different event.

Hornbein

I've been wondering about a simple question that I can't just google and get the answer to. Usually when we calculate probability, we know the number of possible outcomes. Say we toss a coin, there are 2 possible outcomes with one being head and one being tail. So the chance of getting a head is 1/2, WHEN you toss the coin. So maybe "tossing the coin" is a defined event. What if the event is continuous in time? What if say, instead of tossing the coin, I balance the coin so it rolls down the hills, and I ask the question, what is the chance of the coin losing its balance after rolling down the hills for 10 seconds, for 20 seconds, and so on? A more practical example would be what is the chance of getting into a car accident after driving for x amount of time? I would expect the theory that corresponds to this to be a growth of probability with respect to time where it reaches 100% when t->infinity.
The Poisson distribution is what you are looking for.

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