After taking out the first mouse (a brown one), there are 9 mice remaining in the cage, 4 white ones and 5 brown ones. The probability, then, that the second mouse will be a white one is computed as follows:
P = (Number of White Mice Remaining in the Cage) / (Total Number of Mice Remaining in the Cage)
Notice that the answer will depend on the manner she takes mice out. If she takes them one after another, then Robert's answer is correct. If she takes both together (with two hands, for example) then the probability is: