Problems like the Monty Hall problem and the birthday paradox show that human intuition about probability is terrible. Our gut feelings about chances are often completely wrong. Is there an evolutionary reason why our brains struggle so much with probability?
Probability feels counterintuitive because our brains are better at stories than at base rates.
In daily life, one vivid example often feels stronger than a large statistical pattern. That is useful for quick survival decisions, but it creates mistakes in probability.
Three common traps are:
If a coin lands heads five times, we feel tails is "due," but independent flips do not remember the past.
If 10 people win a lottery, that sounds common until you ask how many millions entered.
The probability of evidence given a cause is not the same as the probability of a cause given the evidence. This is why medical tests and courtroom statistics can mislead people.
That is why examples like Monty Hall and the birthday paradox feel wrong at first. They force us to count the sample space carefully instead of trusting intuition.
What about complex numbers? Do the same rules apply in that context?