An experiment is performed where a coin is flipped until the first Head appears. The coin is biased. The probability of seeing a Tail is 5 times as likely than seeing a Head. If X denoted the number of time the coin is flipped when the first head is observed, determine the probability function and validate (i.e. if you flip a Head on the first flip, X=1) Solution Let H-T-T-H represent the event of getting head, tail, tail, then head. (and so forth) We are given: P(H) = 1/6 P(T) = 5/6 so... P(X=1) = P(H) = 1/6 P(X=2) = P(T-H) = 5/6 * 1/6 P(X=3) = P(T-T-H) = 5/6 * 5/6 * 1/6 ... P(X=n) = P(T-...n-1 T\'s total...-T-H) = 5/6 *...n-1 terms of 5/6 total... * 5/6 * 1/6 = (5/6)n-1 * 1/6 = 5n-1/6n Therefore: P(X=n) = 5n-1/6n.