1) A group of n people of different heights are randomly ordered. Given that the very shortest person is first and the very tallest person is last, what is the probability the intermediate one are ordered by increasing height?
2) For fixed B with P(B) >0, show that P(*/B) satisfies the three probability axioms. That is, a) P(A/B) >= 0 for every A. b) P(Owmega/ B) =1 c) For a disjoint union Ui Ai P(Ui Ai/B) = Sigma i P(Ai/B).
3) A poker player holds 3 kings and awaits being dealt two more cards. what is the probability that those two cards are a pair so that the final five card hand is full house?