I have time intervals and probabilities for an event to occur in these time intervals. I want to calculate the probability of the event happening once or more during the entire period, that is to say with an event $X$, I want to know $P(X \geq 1)$ across all of the time periods specified. The probabilities can be assumed to be independent of each other.
I'll illustrate with example data:
Time_bin Probability 0 <= t < 1 70% 1 <= t < 2 30% 2 <= t < 3 10% 3 <= t < 4 50% 4 <= t < 5 20% Total: Total: 0 <= t < 5 ?
I have been thinking about using a binomial distribution somehow, but I really don't know how I would go about that. Any pointers would be greatly appreciated.