Problem 11 Solution: "You've Been Blocked"

Problem 11a.

There are 27 possible combinations (3^3) of 3 block cards. There are 6 ways of having three different block cards, so the probability of blocking a mixed combo of that type is 6/27. Given a particular range of attack coming in, there is only 1 way of having three block cards all of that type, so the probability is 1/27.

Problem 11b.

Out of the 27 possible combinations of block cards, only 8 of them (2^3) do not have any medium block cards (there's 2 possible choices for each of the 3 cards). Thus there is a 19/27 probability of a successful block.

Problem 11c.

There are 7 possible combinations of block cards that have two or more medium block cards, and 19 that have at least one. Therefore, given that the attack was blocked, there is a 7/19 chance that there is another medium block card in his hand. If there isn't, there is a 1/3 chance that he will draw a medium block card on his next turn. Therefore the chance of him having a medium block card is 7/19 + (1/3 * 12/19) = 11/19.