# Enumeration:Combinatorics [closed]

Every new year, Dr Zookh ponders whether she should give up being an evil genius and turn her life around. She flips her lucky coin: heads means “yes, become a better human being”, tail means “no, continue being an evil genius”. Heads and tails are equally likely on the lucky coin. (a) Since Dr Zookh is an evil genius, she will actually flip the coin until she gets tails and then stop. What is the probability that she needs to flip the coin precisely n times? [Hint: How many different sequences of n coin flip outcomes are there? How many of these would lead Dr Zookh to stop after n flips (and no sooner)?]

• Try working out the problem for small values of $n$ to see if you detect a pattern. – N. F. Taussig Jun 10 at 18:33