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Math Help - Adding up probabilities

  1. #1
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    Adding up probabilities

    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
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  2. #2
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    Quote Originally Posted by TheRobster View Post
    What formula/approach do I need to use to work out the probability of at least one event occuring out of several events?
    At least one is the complement of none.
    One minus none is at least one.
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  3. #3
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    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.
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