If they say “50% chance of rain” and it’s raining where you are, there’s a 50% chance that you’re hallucinating.
Yeah, but how was that percentage computed? I agree with your statement and it answers the op but does not explain how the percentage was derived. Cecil’s comments and other comments here indicate historical data are compared with present conditions and by using a computer, the percentage is determined. Many factors are in play in determining if it will rain at any locale and the intensity of the rain. Here in Charleston, SC we get heavy rain storms from all directions. If the storm is crossing the mountains, the intensity of the rain, if it rains at all, will be reduced. If coming from the ocean it will not. Meteorologists know the history of what an air mass will do based upon current conditions. Often the rain headed our way are fragmented (showers) and so there is not a 100% chance of rain in any one area, but the percentages are computed based upon many factors, such as the terrain, is the air mass heading into a dry pocket, is it daytime when convections will occur, etc.
In theory, if you look at all the days on which a 10% chance of rain was predicted, it should have rained on 10% of them. The particular tools used to make that forecast (satellite images, computer models, etc.) are at the forecaster’s discretion. Of course, that’s a murky definition, since a forecast is for a large area, and it might have rained in only part of that area, and you have to define how much water constitutes “rained”, but that’s the basic idea.
In practice, “retail” forecasts are biased wet, presumably because people are angry when it unexpectedly rains, but happy when it unexpectedly doesn’t.