So... if there is a 10% chance that there will be a 25% cost overrun, and a 90% chance that the unexpected expenses will fall within the contingency budget, should the budget be 125% projected cost, or 102.5% projected cost?

Which is entirely the wrong way to go about the problem. If this project is critical, and it's failure will sink the company, you really, really want to be in a position to handle the 25% cost overrun. If you have ten other identically-sized, identically-important project, then the 102.5% estimate is probably going to give you enough of a contingency to handle any one of them going over budget (but what is your plan if two go over budget?)

Thinking in terms of statistics, without any actual details attached, is one of the BIG failure modes I see from rationalists - and one that laypeople seem to avoid just fine, because to them the important thing is that Project X will make or break the company.

Keep in mind that meetings will expand to fill the allocated time, even if they are completed before then, and projects will tend to use their entire budget if possible.

I'd suggest that this is a solvable problem - I've worked in multiple offices where meetings routinely ended early. Having everyone stand helps a lot. So does making them a quick and daily occurrence (it becomes routine to show up on time). So does having a meeting leader who keeps things on-topic, understands when an issue needs to be "taken offline" or researched and brought up the next day, etc..