In a game of poker, Ike Clanton lost 12 hands in a row to Doc Holliday. He claimed,

"Nobody is that lucky," while Doc pointed out that maybe poker was not Ike's game.

(a) Assume in each game Ike was equally likely to win or lose. Compute the probability

of 12 consecutive losses. What crucial assumption are you making?

(b) Assume Ike's winning probability was 30 percent in each game because of his poor

poker skills. Compute the probability that during 12 consecutive games, Ike won two or

more times.

(c) Suppose the game was rigged, and that Ike's winning probability was only one percent

in each game. Compute the probability that in a sequence of games, Ike's first win occurred

after the 12th game.