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I am trying to calculate the probability that any a number events will occur. For instance you have 5 events that a 75% chance of happing how do you calculate the probability that any of the five will occur (be true)?

In my case I have a list of universities I want to apply to; given their acceptance rates I'd like to find my chance of success/failure. But I'll spare you the details. I really ought to know the math behind this. However I have found most explanations of this utterly unhelpful.

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The chance that at least one event happens is the complement of the product of the chances that each of them doesn't happen, assuming they are independent. So if you have events with probabilities $p,q,r$, the chance of at least one is $1-(1-p)(1-q)(1-r)$ I repeat: this assumes they are independent. There is probably some correlation between university A accepting a student and university B doing so.

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@DavidMitra: fixed –  Ross Millikan Feb 12 '13 at 22:38
    
Then I ask, How does one effectively model the relationship between grades/test scores with acceptance rates ? –  Python Feb 12 '13 at 22:44
    
@Python: years ago universities would publish a grid of grades and GRE score with the acceptance rate in each cell representing a certain range. Maybe they still do. That is better than averaging over the whole population. But suppose there is a student with mediocre grades/test scores who has published a respected paper. S/he will may be admitted everywhere. This is the sort of correlation I was talking about. –  Ross Millikan Feb 12 '13 at 22:52

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