Source: A Quant Company Placement Test 2010 at IITB
Problem: 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.
Update (Oct 30, 2010):
Solution posted by Ankush Agarwal (Junior Undergraduate, CSE, IITB) in comments!
Update (Nov 05, 2010):
A different solution posted by Piyush Sao (5th year Dual Degree Elec Student, IIT Madras) in comments!