Compute P$($A $=$ true $|$ X $=$ true, B $=$ false$),$ given that

P$($A $=$ true$)=0\mathrm{.}4,$ P$($X $=$ true $|$ A $=$ true$)=0\mathrm{.}3,$ P$($X $=$ true $|$ A $=$ false$)=0\mathrm{.}2,$ P$($B $=$ true $|$ A $=$ true$)=0\mathrm{.}5,$ P$($B $=$ true $|$ A $=$ false$)=0\mathrm{.}4$

Return the answer $($rounded$)$ up to $2$ decimal places.