What is the Probability of A' n B' Given A' and A, B, and A n B?

Thread starter hellokitten
Start date Oct 8, 2015
Tags

Probability

AI Thread Summary

The discussion focuses on calculating the probability P(A' n B' | A') using known probabilities P(A), P(B), and P(A n B). It establishes that P(A u B) can be derived from the formula P(A) + P(B) - P(A n B). The calculation simplifies to P(A' n B' | A') = [1 - P(A u B)] / P(A'). The final expression is confirmed as [1 - P(A u B)] / [1 - P(A)]. The discussion concludes with a verification of the derived formula's correctness.

Oct 8, 2015

hellokitten

Given P(A), P(B), and P(A n B) . Find the P(A' n B' | A')
We know P(AuB) = P(A)+P(B)- P(A n B)
Then
P(A' n B'|A') = P(A' n B' n A' ) / P(A') = P(A' n B') / P(A') = P(A u B)' /P(A') = [1-P(A u B) ]/ P(A') =
[1-P(A u B)] / [1-P(A)] Correct?

Physics news on Phys.org

Oct 8, 2015

FactChecker

Science Advisor

Homework Helper

Right

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...

View full post »