確率論
Iレポート問題
2013/12/04, 西岡
• このレポートの成績は出席点に加点する. よって提出は任意である.
• レポートの締め切りは, 2014年01月09日(木), 20時. 商学部事務室に提出のこと.
• 体連所属者は部活を明記した場合,共同提出を認める. それ以外は各自単独で提出のこと.
(∗) 以下の各々の問題の概要を記述し,設問に答えよ. なお, その解答に到達した理由も記述する こと.
Problem 1. You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.
You randomly pick a bag and take out one marble. It is a white marble. Then what is the probability that the remaining marble from the same bag is also white?
Problem 2. Five pirates of different ages have a treasure of 100 gold coins. On their ship, they decide to split the coins using this scheme:
(i) Theoldest pirateproposes how to share the coins, the other pirates (not including the oldest) will vote for or against it.
(ii) If 50% or more of the pirates vote for it, then the coins will be shared that way.
(iii) Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.
Let us name the pirates (from oldest to youngest) as Alex, Billy, Colin, Duncan and Eddie. At first, Alex proposes a 97 : 0 : 1 : 0 : 2 split. Then what will happen? More precisely, say that who vote for him with what reason. Here assume that all five pirates are intelligent, rational, want to get as many as possible, and do not wish to die.
Problem 3. A man is caught on the King’s property. He is brought before the King to be punished. The King says, ”You must give me a statement. If it is true, you will killed by lions. If it is false, you will be killed by trampling of wild buffalo.”
But in the end, the King has to let the man go. What was the man’s statement?
