How to apply bayes rule for this problem?

Question

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.

Answer 1

Use Bayes: $$P(X=T|Y=F)=\frac{P(Y=F|X=T)P(X=T)}{P(Y=F)}$$

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

Answer 2

To begin: $\mathsf P(X=T\mid Y=F) ~{= \dfrac{\mathsf P(X=T,Y=F)}{\mathsf P(X=T,Y=F)+\mathsf P(X=F,Y=F)}\\~\\\vdots}$