a little information often tells you a lot

A lot of people demand way too much evidence for things before they will believe them. Some of this is related to a desire for certainty, rather than a probabilistic view of the world. You can get caught up in frequentist statistics and take it way too far. Conditional probability and/or Bayesian logic is much more useful. Even conditional on that (lol), most people don’t update their beliefs nearly enough when they get new information. A small amount of information often moves conditional probabilities and extreme amount. Some conditional probability is easy and obvious. If we walked into a random room of 30 people, the probability any of them could do 500 pushups without stopping is very small, maybe I would lay you 200-1 or more on a bet. But if someone walked up to us randomly and out of nowhere wanted to bet he could do 500 pushups without stopping, we’d be crazy to even take the bet at even money. Conditional on wanting to bet, the probability he can do the push-ups goes from…