Conditional Independence

One of the most powerful tools to reduce complexity.

• $\Pr(\mbox{\rm happy}) = \Pr(TT)+\Pr(TF) = 0.40.$
• $\Pr(\mbox{\rm happy}\vert\mbox{\rm stock}) = \Pr(TT)/(\Pr(TT)+\Pr(FT)) = 0.40$

Can specify the same information using just two numbers:

• $\Pr(\mbox{\rm happy}) = 0.40.$
• $\Pr(\mbox{\rm stock}) = 0.20.$