Quick Answer: Humans did not evolve to understand statistical probability; we evolved to survive immediate, vivid threats. Consequently, we drastically overestimate the probability of rare, dramatic events (plane crashes, terrorism, shark attacks) and severely underestimate the probability of common, boring events (heart disease, car crashes, diabetes).
The Availability Heuristic
When judging risk, the brain asks a shortcut question: "How easily can I think of an example of this happening?" If examples come to mind quickly, the brain assumes the probability is high. News media reports continually on plane crashes and rare diseases, making them highly "available" in memory. Car crashes are too common to report on nationally, making them "unavailable," leading us to feel safer in a car than a plane (despite the math proving the opposite).
The Illusion of Control
Humans rate risks as much lower if they feel they are in control. When you drive, you possess the steering wheel. The perceived probability of crashing feels low. In an airplane, you have zero control, causing the perceived risk to skyrocket. This illusion bypasses statistical reality.
The Micro-Probability Blindspot
The human brain cannot comprehend the difference between a 1-in-100,000 risk and a 1-in-100,000,000 risk. Both just register as "a tiny chance, but it could happen." This makes it incredibly difficult to make rational decisions about extreme long-tail risks, insurance policies, or lottery tickets. To the brain, buying a ticket turns an impossibility into a possibility, which feels emotionally satisfying despite the EV being heavily negative.
Overcoming the Defaults
To make rational risk decisions, we must manually override our instincts using data. Instead of asking "Does this feel dangerous?", we must ask "What is the base rate frequency of this event in the population?" Check the math, ignore the news cycle.