Most of us don’t do well on thinking tasks that incorporate uncertainty and probability. Not only do we not always get the answer right, there are forces in our brain actively pushing us towards incorrect answers.
I like the example of the weather because it’s something we all deal with in day to day life. Say you read a weather forecast and it says there’s a 30% chance of rain today. That’s a far more complex and subtle statement than either “It will rain,” or, “it won’t rain.” It’s also difficult to understand what it means for that statement to be true or false. Because 30% is less than fifty-fifty so it’s leaning towards not-rain. So if it rains is the statement false? If it doesn’t rain is the statement true? Clearly neither of those is quite correct, so is the statement meaningless?
The reason it’s confusing is that there are multiple ways for the statement to be wrong. First, the equipment could be broken. So there is a large rain cloud but the particular satellite that was supposed to be looking at it was turned off. Second, the forecast could be wrong. Perhaps the system was giving them information in kilometres per hour but the map is measured in miles so they know about the rain cloud but are wrong about what day it will rain.
The other way it’s possible to be wrong is to incorrectly factor in the consequences of the prediction. So if there is a 30% chance of rain, wearing the $400 pair of suede boots that will be destroyed by puddles is clearly a mistake, but it’s a mistake in how a probability is paired with it’s consequences which is hard. “What is the dollar value of a 30% chance or ruining a $400 pair of shoes?” that doesn’t have a trivial answer.