Sample Question #265 (probability brainteaser)
Consider a coin with the probability of getting heads being p, where p>=0.5. You toss the coin and get a tails on the first toss.
1) What is the expected number of tosses needed to get an equal number of heads and tails for the first time?
2) Will your answer be the same if the first toss gave you heads?
3) What is your answer if p<0.5?
(Comment: this is a classic problem and is quite difficult)