What is the Definition of precipitation chance?

Answer 1

Definition: The probability of precipitation in a weather forecast is an estimate of the chance of a measurable amount of rain or snow falling anywhere in a given forecast region over the forecast period. Probabilities are given in 10 percent increments.
Ref: http://canadaonline.about.com/cs/weather/g/pop.htm

UNDERSTANDING POP (CHANCE OF PRECIPITATION)

POP is the probability of any particular point location within a forecast area receiving measurable precipitation in a given time period. POP is determined by two parameters: The probability that any precipitation will occur in forecast area AND predicted areal coverage of precipitation if precipitation does occur. Thus, areal coverage is just one aspect of POP. The chance that any measurable precipitation will occur in the first place within the forecast area must also be considered. When referring to POP it is most accurate to say, "There is a ___% POP that any particular measurement station in the viewing area will get precipitation". For example, when averaged over many 30% POP days, a particular station should have precipitation 30% of the time if the forecaster or computer model is accurate.

Suppose during the course of a year that a Dallas measurement station has a 30% POP on 100 individual days. If the POP prediction is fairly accurate over the long term, it should have precipitated at the Dallas station on about 30 of those days. Thus, think of POP in terms of a long term average prediction. All to often, people assume a 20% chance of rain means 20% of forecast area will get rain on that one day. This is often not the case for any one day. Often no precipitation occurs at all in the forecast area on days with a 20% POP since one component of POP is the chance that any precipitation will develop.
Ref: http://www.theweatherprediction.com/habyhints/284/

Probability of Precipitation

A Probability of Precipitation or POP is a formal measure of the likelihood of precipitation that is often published from weather forecasting models.

In U.S. weather forecasting, POP is the probability that more than 1/100th of an inch of precipitation will fall in a single spot, averaged over the forecast area.[1] For instance, if there is a 100% probability of rain covering one side of a city, and a 0% probability of rain on the other side of the city, the POP would be 50%. A 50% chance of a rainstorm covering the entire city would also lead to a POP of 50%.

Note that the POP measure is meaningless unless it is associated with a period of time. U.S. forecasts commonly use POP defined over 12-hour periods (POP12), though 6-hour periods (POP6) and other measures are also published.

The mathematical definition of Probability of Precipitation is defined as:

PoP = CxA[2]
C = the confidence that precipitation will occur somewhere in the forecast area.
A = the percent of the area that will receive measurable precipitation, if it occurs at all.
For example; a forecaster may be 40% confident that under the current weather conditions that precipitation will occur, and that should rain happen to occur it will happen over 80% of the area. This results in a PoP of 32% ((0.4x0.8)x100 = 32%)

Ref: http://en.wikipedia.org/wiki/Probability_of_Precipitation