For the given 200 g of 95% ethanol solution, ethanol is 190g and water is 10g. We determine the number of moles per component.
ethanol: (190 g ethanol) / (46 g/mole) = 4.13 moles
water: (10 g water)/(18 g/mole) = 0.55 moles
Total moles of the solution is 4.68 moles
Mole fraction of water: = 0.55 moles/4.68 moles = 0.117