I'd say an expert in any field has better intuitions (hidden, unverbalized knowledge) than what they can express in words or numbers. Therefore, I'd assume that the decision that it's not worth doing the examination should take priority over the numerical estimate that he made up after you asked.

It may be better to ask the odds in such cases, like 1 to 10,000 or 1 to a million. Anyway, it's really hard to express our intuitive, expert-knowledge in such numbers. They all just look like "big numbers".

Another problem is that nobody is willing to put a dollar value on your life. Any such value would make you upset (maybe you are the exception, but most people probably would). Say the examination costs $100 (just an example). Then if he's 99.95% sure you aren't sick, and 0.05% sure you are dying and sends you home, then he (rather your insurance) values your life at less than $200,000. This is a very rough estimation, but it seems in the right ballpark for what a general stranger's life seems to be valued by the whole population. Of course it all depends on how much insurance you pay, how expensive the biopsy is etc. Maybe you are right that you deserve to be examined for your money, maybe not. But people tend to avoid this sort of discussion because it is very emotionally-loaded. So we mainly mumble around the topic.

People are dying all the time out of poverty, waiting on waiting lists, not having insurance, not being able to pay for medicaments. But of course people who have more money can override this by buying better medical care. Depending on the country there are legal and not-so-legal methods to get better healthcare. You could buy a better package legally, put some cash in the doctor's coat, etc.

You need to consider that the people who'd do your biopsy can do other things as well, for example work on someone's biopsy who has a chance of 1% of dying instead of your 0.05% (assuming this figure is meaningful and not just a forced, uncalibrated guess).

If you confronted your doctor with these things, he'd probably prefer to just revoke that probability estimate and just say his expert opinion is that you don't need the biopsy, end of story. It would be very hard for you to argue with this.