Problem: This is problem 33 of section 2.6 (conditioning) in Bertsekas, Tsitsiklis Introduction to Probability 2nd:
We are given that a coin has probability of heads equal to p and tails equal to q and it is tossed successively and independently until a head comes twice in a row or a tail comes twice in a row. What is the expected value of the number of tosses?
I don't understand the answer. Why $$E[X\mid H1,T2] = 1+E[X\mid T1]$$ Is there any relationship? Thanks!