What is the expected number of coin flips to get two consecutive heads?

What is the expected number of coin flips to get two consecutive heads?

Approach: Set up recurrence relation using states based on current streak of heads.

Let E be expected flips from start, E_H from state of having one head. E = 1 + 0.5*E + 0.5*E_H. E_H = 1 + 0.5*0 + 0.5*E. Solving gives E = 6.

Follow-up: What about k consecutive heads?

Key concepts: expected value, recurrence, states.