# Probability over a period of time

• cdux
In summary, if you want to see if an event will happen in subsequent runs, you need to calculate the probability of it happening given the current probability and then compare it to the desired probability.
cdux
Say I have the probability of something happening in period of a day. How am I going to tackle finding the probability of it happening in a period 7 days? Statistical independence of events or not.

If they are independent it is easy. Let p = prob(event in one day), q=1-p. Then the prob of not happening in seven days is q^7, so prob happening at least once in 7 days is 1-q^7.

does that derive from a union of independent events?

cdux said:
does that derive from a union of independent events?
No. q^7 comes from the intersection of independent events.

Ok, I think I understand the logic now. ty.

mathman said:
If they are independent it is easy. Let p = prob(event in one day), q=1-p. Then the prob of not happening in seven days is q^7, so prob happening at least once in 7 days is 1-q^7.

Then how is (1-0.1)^3 = 0.729
and (1-0.9)^3 = 0.01 (only)?

(assuming an event of 0.1 (and it not happening of 0.9))

EDIT: Oh, it may be I guess that the closer to 1 a probability is, the more likely to occur[in subsequent runs] in an exponential fashion, whereas the closer to 0, the less likely in a reversely exponential fashion.

Last edited:
I am not sure what you are trying to do. It looks like you are calculating probabilities for these two events: happening every day or never happening at all. Obviously they don't add up to 1.

Note (1-0.9)^3=0.001

cdux said:
Then how is (1-0.1)^3 = 0.729
and (1-0.9)^3 = 0.01 (only)?
Actually (1- 0.9)^3= 0.001.

(assuming an event of 0.1 (and it not happening of 0.9))

EDIT: Oh, it may be I guess that the closer to 1 a probability is, the more likely to occur[in subsequent runs] in an exponential fashion, whereas the closer to 0, the less likely in a reversely exponential fashion.

No, they are not equivalent (and being "closer to 1" has nothing to do with it).

If you have an event that has a probability of 0.1 of "happening" in a given trial, and so a probability of 0.9 of "not happening", then (1- 0.1)^3 is the probability it does NOT happen in three consecutive trials. (1- 0.9)^3= 0.1^3 is the probability it DOES happen in all three trials. They don't add to 1 because there are many other things that could happen: happen in the first trial but not in either of second or third trials, happen on the first and third trial but not on the second trial, etc. "happen on all trials" and "happen on no trials" do not exhaust all the possible outcomes.

I understood what I didn't understand a while after the last post of mine.

Simply: 1-(1-"probability_of_what_we_try_to_see_IF_IT_WILL_HAPPEN in_n_subsequent runs")^n

i.e. if I put 0.01 there I try to see if that will happen in n runs. but if I put its complimentary 0.99, I'll be solving ANOTHER PROBLEM, trying to see if its complimentary will happen in n runs.

## 1. What is probability over a period of time?

Probability over a period of time is the likelihood or chance of a certain event occurring within a specific timeframe. It takes into account the probability of an event happening at any given moment during the period of time.

## 2. How is probability over a period of time different from regular probability?

Regular probability only considers the likelihood of an event happening at a specific moment, while probability over a period of time takes into account the probability of the event happening at any point during the designated time period.

## 3. How is probability over a period of time calculated?

To calculate probability over a period of time, you would need to multiply the probability of the event occurring at any given moment during the time period by the length of the time period. This gives you the overall probability of the event happening within the designated timeframe.

## 4. Can probability over a period of time change?

Yes, probability over a period of time can change if the probability of the event happening at any given moment changes or if the length of the time period changes. It can also change if new information or variables are introduced.

## 5. How is probability over a period of time used in scientific research?

In scientific research, probability over a period of time is often used to analyze and predict the likelihood of certain events occurring within a given timeframe. It can also be used to compare the probability of different events happening over the same period of time.

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