You are given an urn with 100 balls (50 black and 50 white). You pick balls from urn one by one without replacements until all the balls are out. A black followed by a white or a white followed by a black is "a colour change". Calculate the expected number of colour changes if the balls are being picked randomly from the urn. Hint
There are 99 positions. Let X_i be a random variable taking value 1 if i_th position has a colour change and zero otherwise.
We have to find expected value of E[X_1 + X_2 + ... + X_99]
Since all X_i are equivalent, the answer is 99*E[X_i]
E[X_i] = ((50/100)*(50/99)+(50/100)*(50/99)) = 50/99
So, Answer is 50.