1

I am trying to understand the solution on how to compute the number of expectation to get three consecutive heads of a fair coin. The solutions says let $E$ be the expectation. Then $$ E = \frac{1}{2}E + \frac{1}{2} (E + 1) + \frac{1}{4} (E + 2) + \frac{1}{8} (E + 3) $$ and solving this equation one gets $E = 14$.

I am struggling to understand how this works. It seems that we just start at count $E$... any clarification appreciated.

Johnny T.
  • 2,897

1 Answers1

1

Where does this come from? Does it give $14$ as a solution?

It is not the equation I would have written, but instead $$E=\frac12(1+E)+\frac14(2+E)+\frac18(3 +E)+\frac18(3)$$ since you flip

(a) a tail and start again or

(b) a head and a tail and start again or

(c) two heads and a tail and start again or

(d) three heads and stop.

Henry
  • 157,058