A fair coin is flipped repeatedly. What is the expected number of flips until you get two consecutive Heads (HH)?
Show answer & explanation
Correct answer: C
Explanation
Let E be the expected number of tosses to get HH.
Let F be the expected number of tosses after getting one H (i.e., the last toss was H).
E = 1 + (1/2)F + (1/2)E
E = 2 + F
F = 1 + (1/2)0 + (1/2)E
(Getting an H results in HH; otherwise, getting a T returns the process to the initial state.)
F = 1 + E/2
E = 2 + 1 + E/2
E/2 = 3
E = 6