Abstract Thoughts on the Chance of Rain

I have a day in mind, but I'm not telling you. My question is: what is the chance that it rained that day in Washington DC?

You have no knowledge of the cloud formations, temperatures, or time of year. However, suppose that over the last four decades, it rained 15% of the time in DC. So your best guess is 15%, but you're not very confident.

Suppose that I told you that my mystery day was in September. You could look at historical September predictions and adjust your guess accordingly, now with slightly more confidence.

Yet when we look at the 10-day forecast, we routinely see that the chance of rain is around 50%. This could mean that, historically, it has rained about 50% of the time during this time of year. More likely, it means that historical patterns mean very little when we want to know if it will rain any particular day; instead, the forecast is primarily influenced by the latest meteorological readings.

If it's for sure not going to rain tomorrow, the chance is 0%. If it's for sure going to rain, the chance is 100%. It's amazing to me that, given modern technology, we so often see chance of rain predictions for the very near future around 50%, essentially a coin flip.