Also, as a fun side observation, this sounds suspiciously like a test designed to figure out which of us actually thinks we're >99% once we take into account the other opinion and which of us is only >99% before we take into account the other opinion. Dr. House might be thinking that if we order 15k of either medicine that one is right often enough that his work here is done. I'd have to assign that p>0.01, as it's actually a less evil option than taking him at face value. But I'm presuming that's not the case and we can trust the scenario as written.

I wasn't going there, but I like the thought =)