This is not a math problem. This is purely a language interpretation problem. Someone makes a statement and immediately contradicts it, leaving the audience in a state of confusion which props them to blindly guess what the person is thinking. Blindly guessing what someone is thinking is not a math problem. The statistics are irrelevant beyond the intended purpose of communicating that someone contradicts himself without explanation. The context could contain 100 mathematical formulae, or one million, or none at all, the doctor's statement "don't worry" will always be the solve driving cause of dissent. All mental efforts are spent solely to investigate what that statement alone is trying to say. This can be proven quickly: just rewrite the problem and keep the same math components, change only the doctor's opinion.
>"Sir, the surgery has 50% survival rate"
>"My last 20 patients have all survived"
>"You should be worried"
The doctor's communication is now easy to understand. They say that the surgery is dangerous and they evidently believe their own statement. It is only when the doctor tells you to not worry, when they appear to not believe their own statement, that something doesn't seems right with the communication, thus leading to a language interpretation problem. We are compelled to attempt to guess what the doctor is thinking. Does the doctor not understand what a survival rate means? Is the doctor incorrectly communicating that the survival rate is alleged, outdated or untrustworthy? Is the doctor succumbing to the gambler's fallacy? Does he thinks dying is fun? We don't know, we can only guess, and no amount of math knowledge will tell us which guess is correct, because this is not a math problem.
