That out of 100%, there is a 15% chance of rain (if it helps think of it as 15 out of 100 points). So very unlikely it will rain
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There is a 10% chance of any form of water falling from the sky.
A forecast that says, for instance, "there is a 10% chance of rain tomorrow," means that on 10 out of 100 days with weather conditions very similar to the conditions expected tomorrow, at least a trace of train has occurred. Some will disagree with this answer for various reasons. For the results of research that evaluated how understanding of percentage chance of precipitation varies around the world, see "A 30% Chance of Rain Tomorrow: How Does the Public Understand Probabilistic Weather Forecasts?," available as a PDF file via the URL http://www.mpib-berlin.mpg.de/en/mitarbeiter/gigerenzer/pdfs/RainFinal.pdf .
99.9 CI means that there is a 99.9% chance the CI limits contains the value you are looking for.
Roughly 1.2 percent chance
There needs to be a location as well as a time interval. A statement such as "there is a 40% chance that it will rain in Yourtown over the 12 hours starting at sunrise tomorrow" means that if you consider a whole lot of days like tomorrow - with the same sort of weather as you experienced over the last few days - then in 4 days out of 10 (40%), it will rain tomorrow. Just to complicate matters, the statement does not distinguish between there being a 40% probability that it will rain non-stop or that it will rain briefly.