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

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

Approach: Set up recursive equations for states.

6. Let E be the expected flips. E = 1/2(E+1) + 1/4(E+2) + 1/4(2). Solving gives E=6.

Follow-up: What is the expected number for H-T?

Key concepts: recursive expectation, absorbing states.