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Probability of rain this weeken?

  1. Oct 29, 2011 #1
    Probability of rain this weeken??

    If there is a 50% chance of rain on saturday, and the same on sunday, what's the probability of rain this weekend? The answer apparently is 75%, because three of four scenarios have rain. Following this theory, wouldn't you get the same answer if you asked "what's the probability of NO rain this weekend" ?
     
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  3. Oct 29, 2011 #2

    Simon Bridge

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    Re: Probability of rain this weeken??

    Almost.

    The only way you'd say "there was no rain this weekend" would be if it was fine all weekend.

    This is why statistitians are usually much more precise in their language, vis:
    There is a 0.75 probability that there is rain on at least one day this weekend
    There is a 0.75 probability that there is at least one fine day this weekend but only 0.25 probability that it is fine all weekend long.

    Similarly, there is only 0.25 prob that it will rain both days.

    Of course, this calculation assumes that the rainfall events are independent.
     
  4. Oct 29, 2011 #3
    Re: Probability of rain this weeken??

    Yes. Treating weather events closely related in time as independent events is inappropriate. Lacking a fully deterministic theory for such events, correlations are determined from long term data.
     
  5. Oct 29, 2011 #4

    Simon Bridge

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    Re: Probability of rain this weeken??

    John Paulos (Innumeracy) uses the problem as an example... there it is represented as a reaction to a weather report: there's a 50% chance of rain on Saturday and a 50% chance of rain on Sunday, so there is a 100% chance of rain this weekend.

    But what did the meteorologist mean? Perhaps there was, indeed, going to be rain in the weekend with equal chances of falling on either day? This, or something like it, may well have been the case if that worthy had indeed taken into account long-term data. So perhaps John shouldn't have scoffed?
     
  6. Oct 29, 2011 #5
    Re: Probability of rain this weeken??

    This is just ignorance of probability on Paulos's part. If the events were independent, the probability of rain on the weekend is the sum for two independent events:

    0.5 + 0.5 - (0.5)(0.5) = 0.75

    Also, it's not just long term data involved in predictions. There are good theories about the behavior of weather systems, but predictions always carry a degree of uncertainty.
     
    Last edited: Oct 29, 2011
  7. Oct 30, 2011 #6

    Simon Bridge

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    Re: Probability of rain this weeken??

    Somehow I doubt that :)
    http://en.wikipedia.org/wiki/John_Allen_Paulos
    ... he was using as an example of the sort of mistake he sees often.
     
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