Factoring Probability: A Conversation

Francis: Let's say you are a scientist.
Franky: OK, I am a scientist.
Francis: Good. Now let's say that you have 5 theories.
Franky: I have 5 theories. [Giggle]
Francis: Let's give these theories a collective identity.
Franky: A name?
Francis: Yeah. Let's call it, "The H.I.A.S. Theory."
Franky: Hias?
Francis: Bear with me. Now these 5 theories are accurate. Let's say they are accurate within 90%.
Franky: 9 out of 10 is good.
Francis: Pretty good. Now the first theory is accurate to within 90%...
Franky: I'm following you...
Francis: Each successive theory is based on the success of the theory before it. Understand?
Franky: Yes. If A succeeds then B. If B succeeds then C and so on.
Francis: Exactly. Now assuming that the 5th theory is accurate to within 90% what is the likelihood that the 5th theory will work?
Franky: 90%?
Francis: Nope. 54%. It has nearly as good a chance to fail as to succeed.
Franky: Marginally interesting.
Francis: Now if you have 10 theories with a 90% probability rate, all based on the success of the one prior, the 10th theory will have less than a 1/10 chance of working.
Franky: Not too good.
Francis: Nope.
Franky: Can't go with the hias theory then. [giggle]
Francis: But then again, that is How It All Started. And there are thousands of theories, each dependant on the one prior.
Franky: [giggle]
Francis: Let's pretend we're not scientists.