What formula/approach do I need to use to work out the probability of at least one event occuring out of several events?
For example suppose I have 3 events with probabilities of occurance 0.29, 0.32 and 0.45. How do I work out the probability of at least one of these events occuring? I know that you can't just add the probabilties up...
Thanks
If you know the probability that none of the events occur (call this P{none}), then the complement of this is the probability that at least one occurs : P{at least one} = 1 - P{none}.
Now, to find P{none}, there are some assumptions missing. If the 3 events are INDEPENDENT, then we can use the product rule:
P{none} = P{no event 1 and no event 2 and no event 3}
= P{no event 1} * P{no event 2} * P{no event 3}
= (1 - P{event 1}) * (1 - P{event 2}) * (1 - P{event 3})
Remember, you can only do this multiplication when the events are independent.