CP Violation in Quasi-inclusive $B\to K^{(\ast )}X$ Decays

We consider the possibility of observing CP violation in quasi-inclusive decays of the type $B^{-}\to K^{-}X$, $B^{-}\to K^{\ast -}X$, ${\bar{B}}^0\to K^{-}X$ and ${\bar{B}}^0\to K^{\ast -}X$, where $X$ does not contain strange quarks. We present estimates of rates and asymmetries for these decays in the Standard Model and comment on the experimental feasibility of observing CP violation in these decays at future $B$ factories. We find the rate asymmetries can be quite sizeable.