Consider flipping a coin that is either heads (H) or tails (T), each with probability 1/2.  The coin is flipped over and over (independently) until a head comes up.  The outcome space is
\[ \Omega = \{H,TH,TTH,TTTH,\ldots\}. \]

(a) What is \( \mathbf{P}(TTH)\)?

(b) What is the chance that the coin is flipped exactly \(i\) times?

(c) What is the chance that the coin is flipped more than twice?

(d) Repeat the previous three questions for a unfair coin which has probability \(p\) of getting Tails.

[Author Mark Huber. Licensed under Creative Commons]