The rule of multiplication applies to the following situation. We have two events from the same sample space, and we want to know the probability that both events occur.
Rule of Multiplication If events A and B come from the same sample space, the probability that both A and B occur is equal to the probability the event A occurs times the probability that B occurs, given that A has occurred.
P(A ∩ B) = P(A) P(B|A)
So if you try every other idea that pops into your head and nine times out ten you’re wrong then your failures happen 0.5×0.9 = 0.45. So now you see that the odds that you’ll have an idea and that it’ll fail is 0.45.
Well that certainly helps.
I suppose one can twist the odds by never trying anything. This removes the chance of any of them failing so in theory all of your ideas are successful. In theory…