If you have a given probability for a specific outcome in a specific event or period of time, how can you calculate the probability of it happening over a length time or number of events?
I've seen answers that might explain what I'm talking about, but I don't understand the notation.
If I have a 10% chance of something happening in a given day, it is NOT a 100% chance over 10 days, but how do you calculate the actual odds?
I thought the way to do it was subtracting the chance it didn't happen from one, for example:
If I have a .1 chance of an outcome on a given day, I think the likelihood of it happening at some point over 10 days is
1-.9^10 which is approximately .65
Did I do this right? Does a 10 percent chance of an outcome per event only have a 65% chance of happening over the course of 10 events?
For a 1% probability over 100 events I tried
1-.99^100 which approximated to 63.4%.
If this is wrong, how do you accrue the likelihood of an event over a number of periods when only the likelihood in a single period is given?