Suppose that in a standard deck of cards (without Jokers), we consider drawing a red King a success. (Note that the probability of this is 2/52 or 1/26). Assume that if a red King is not drawn, the card is placed back in the deck to assure this probability remains at 1/26. Let X be the number of cards drawn until you get a red King.
(a) What distribution does X follow? Completely identify the distribution.
(b) Find the probability that it takes less than 6 draws to get a red King.
(c) Find the probability that it takes 6 or more draws to get a red King.
(d) Find the expected number of draws until a red King is drawn.