## Occasional reflections on Life, the World, and Mathematics

But there is something about their approach that seems to make sense to intelligent people, and not purely idiosyncratic. I’m reminded of Tversky’s famous conjunction fallacy, with studies seeming to show that people’s everyday probability intuitions don’t necessary satisfy the apparently inevitable law of conjunction: The probability of A or B must be bigger than the probability of A and the probability of B. Here we see intuitions of probability that don’t seem to satisfy the law of total expectation: If  are possible future states of the world, and  is the probability of event A conditional on  happening, then the probability of event A now must be some kind of average of these conditional probabilities.