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Homer and Marge play a game by taking turns rolling a standard six-sided die, starting with Homer, until there occurs a sequence of k or more 4s immediately followed by a 5 or 6 (e.g. 45, 245 or 5446, if k = 1). The last person to roll wins the game. (E.g., if k = 2, then each of the sequences 446, 64445 and 465443445 results in Homer winning.) Find the probability that Homer wins, for each k = 0, 1, 2, 3 and 99. 

A stack of ten cards has four hearts (which are red), three diamonds (which are red), two spades (which are black) and one club (which is black). Four cards are sampled from the stack, randomly and without replacement, and placed in a box. Then one card is randomly selected from the box. If that card is a heart then all of the other three cards in the box are burnt. Otherwise, two cards are sampled, randomly and without replacement, from the other three cards in the box, and then these two cards are burnt. Find the probability that exactly k red cards are burnt, for each possible value of k.