3 x 5 = ?

As a kid I was really bothered by the idea that everything is uncertain to some extent, except perhaps that I am - whatever that means. Maybe I was too young when I read Descartes for the first time.
It famously took Whitehead and Russell 379 pages to derive the theorem 1+1=2. But can we be sure that they did not make a mistake somewhere? And how would we quantify the uncertainty of that?

Well, today I had a chance to ask the experts: What is the probability that 15=3x5 is actually false?

added later: In the comments that followed Avi estimated the probability as 1:10^10^100.