I dont know if your question ever got answered, but,
how accurate do you want?
Barometric pressure is actually a good way to predict if it is going to rain. I know the accuracy would deffenitly be much greater than 50% (if 50% is ok, use a coin).

You could hook up a little digital barometer to a comparator, and if the pressure drops enough (low pressure=rain, high=no rain), then a light could come on or whatnot.

This is how it was done in the home for decades (most of our grandpas had them).

"These pressure differences have a big effect on the weather, so if you know the current air pressure at your house, as well as the pressure trend, you are able to predict certain things about the weather. As a very loose rule, a high-pressure area will be clear, and a low-pressure area will be cloudy and rainy. " (http://www.howstuffworks.com/question13.htm)

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