I know Pr(X2 = T | X3 = F) = Pr(X2 = T, X3 = F) / Pr(X3 = F) but I don't know how to figure out each probability individually. Anyone have any idea how to do it?
Assuming T = true, and F stands for false, and that 1-P(T) = P(F)
You need two things here:
- P(X2 = T,X3 = F)
- P(X3 = F)
Let's start with 1. This is equal to P(x3 = F)*P(X3 = F|X2 = T). The second probability is simply 1 - P(X3 = T|X2 = T), which you have.
The second one is more complicated. First you need to use Bayes' Theorem to find P(X2 = T). Then you need to use Bayes' Theorem again to find P(X3 = T). Then you just take 1-(P(x3 = T) to get P(x3 = F).
Hope this helps!