The Weather Forecaster Problem

Suppose you have two forecasts for tomorrow's weather. Forecast A predicts a 60% chance of rain, while Forecast B predicts an 80% chance of rain. If it rains tomorrow, would you consider Forecast B a better forecast than Forecast A? And if so, how much better? If it doesn't rain tomorrow, are both forecasts equally incorrect?

This issue of Everybody's Problems addresses the questions above. What makes a prediction a good prediction? Since predictions are probabilistic rather than deterministic, how can we compare predictions? We have found that our students have very simplistic ideas about probability.

The student's interpretation of what an 80% chance of rain means can be clearly seen in the models that they build to compare weather predictions. The Weather Forecaster Problem makes it very clear that we need to spend more time working with our students on understanding (not computing) probability and probabilistic predictions. We can teach our students to compute probabilities, but that does little to affect their understanding of probabilistic situations.