How to apply bayes rule for this problem? Calculate P(X=T|Y=F) given P(Y=F|X=T) = 0.3, P(X=T) = 0.5, and P(X=F,Y=F)=0.2. Note that T represents true, F represents false, all variables are binary. 

Use Bayes:
$$P(X=T|Y=F)=\frac{P(Y=F|X=T)P(X=T)}{P(Y=F)}$$
And for denominator:
$$
\begin{align}
P(Y=F)&=P(Y=F,X=T)+P(Y=F,X=F)\\
&=P(Y=F|X=T)P(X=T)+P(Y=F,X=F)
\end{align}
$$
