PART 1 - All ABOARD? After centuries of devastating warfare, the rulers of the kingdoms in Westeros and Essos have finally laid down their arms and created a Democratic United World (DUW) where peace and prosperity reign. However, to make sure that history is never forgotten lest it be repeated, the DUW hosts a yearly tournament called the Game of Thrones where representatives from the great houses meet to engage playfully in athletic and intellectual competitions. This year, a ship is carrying competitors from twelve great houses on a long sea voyage from Braavos to King's Landing where the Game of Thrones is being held. The houses that are participating are Targaryen(TAR), Lannister (LAN), Stark (STA), Tyrell (TYR), Baratheon (BAR), Martell (MAR), Arryn (ARR), Tully (TUL), Greyjoy (GRE), Bolton (BOL), Frey (FRE), and Mormont(MOR). In this assignment you are asked to evaluate probabilities relating to this voyage. a) (3 marks) At least how many passengers must this ship carry to guarantee that at least one of the twelve houses will send at least five contestants? Explain your answer. b) (1 marks) The ship was commissioned to make it possible for each of the twelve houses to send exactly five contestants on the voyage. How many passengers does this ship take? Show your calculation. c) (2 marks) Hoping that they would get an early advantage on the tournament, each of the twelve houses has sent six contestants (instead of just five) to the port of Braavos to wheel and deal (and possibly trick) their way onto the ship. No matter what happens, how many of the twelve houses are guaranteed to have at least one contestant board the ship? Explain your answer. PART 1 - All ABOARD? After centuries of devastating warfare, the rulers of the kingdoms in Westeros and Essos have finally laid down their arms and created a Democratic United World (DUW) where peace and prosperity reign. However, to make sure that history is never forgotten lest it be repeated, the DUW hosts a yearly tournament called the Game of Thrones where representatives from the great houses meet to engage playfully in athletic and intellectual competitions. This year, a ship is carrying competitors from twelve great houses on a long sea voyage from Braavos to King's Landing where the Game of Thrones is being held. The houses that are participating are Targaryen(TAR), Lannister (LAN), Stark (STA), Tyrell (TYR), Baratheon (BAR), Martell (MAR), Arryn (ARR), Tully (TUL), Greyjoy (GRE), Bolton (BOL), Frey (FRE), and Mormont(MOR). In this assignment you are asked to evaluate probabilities relating to this voyage. a) (3 marks) At least how many passengers must this ship carry to guarantee that at least one of the twelve houses will send at least five contestants? Explain your answer. b) (1 marks) The ship was commissioned to make it possible for each of the twelve houses to send exactly five contestants on the voyage. How many passengers does this ship take? Show your calculation. c) (2 marks) Hoping that they would get an early advantage on the tournament, each of the twelve houses has sent six contestants (instead of just five) to the port of Braavos to wheel and deal (and possibly trick) their way onto the ship. No matter what happens, how many of the twelve houses are guaranteed to have at least one contestant board the ship? Explain your
