If ever there was a case where this become clear is with the Monty Hall problem. Even the great Paul Erdos got fooled by this problem. My question which may be difficult to answer is what is it about probability that we can be so confident of an answer we get uwing an intuitive argument and yet be so wrong. Benford law on first digits and the waiting time paradox are other famous examples like this.

If ever there was a case where this become clear it is with the Monty Hall problem. Even the great Paul Erdős got fooled by this problem. My question, which may be difficult to answer, is what is it about probability that we can be so confident of an answer we get using an intuitive argument and yet be so wrong. Benford's law on first digits and the waiting time paradox are other famous examples like this.