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일상의 확률문제

 
지은이 : 윤원영, 서순근
출판사 : 경문사
판수 : 1판(2019)
페이지수 : 444
ISBN : 979-11-6073-271-9
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 22,000원
적립금 : 660 Point
   

 
우리는 매순간 다양한 상황에서 판단하고 결정하며 살아가고 있지만, 그때마다 행한 의사결정이 최적일 수 없기에 종종 후회를 한다. “Life is unpredictable and uncertain inthis world. Life here is difficult, short and bound up with suffering”(불교경전인 Sutta-Nipata의 Salla Sutta)라는 삶에 대한 오랜 정의에서도 알 수 있듯이 일상이나 업무에서 항상 예측할 수 없는 수많은 상황에 직면해왔고, 앞으로도 직면하며 살아가야 하는 우리의 어려움을 말하고 있는지도 모른다. 그러므로 우리는 삶 자체가 불확실성하에서의 판단을 요구하고 어떻게든 의사결정을 해야 한다는 사실을 받아들여야 한다. 하지만 정보가 부족하거나 상황이 불확실하여 정확히 결과를 예측할 수 없다고 해서 우리가 할 수 있는 것이 전혀 없거나 대처 불가능한 것은 아니며, 끊임없이 합리적인 판단을 이끌어내어 야 하고 또한 그러한 방법을 찾을 수 있을 것이다.) -머리말 중에서-
제1장 확률계산 문제
1.1 생일이 같은 회원이 있을 확률은 얼마나 될까? (Birth matching and pairing problems) ····································································· 2
1.2 이사 온 옆집의 두 자녀가 모두 아들일 확률은 얼마일까? (Two children problems) ····························································································· 8
1.3 양말 서랍에 몇 개의 양말이 들어 있는가? ····························································· 11
1.4 우리 대학의 등록금은 낮은 편인데 왜 높다고 발표되는가? (Simpson’s paradox) ································································································· 14
1.5 로또 1등에 두 번 당첨된 사람이 있다는 소문은 사실일 수 있는가? ·················· 19
1.6 다음 신기록은 언제 달성될까? ················································································· 23
1.7 이차 방정식에서 실근이 나올 확률은 얼마인가? ···················································· 29
1.8 국회의원 몇 명이 불참 또는 기권하면 법안이 통과되겠는가? ······························ 33
1.9 왜 반대방향으로 가는 엘리베이터가 많은가? ·························································· 37
1.10 그는 서툰 아르바이트생이라고 할 수 있을까? ························································ 44
1.11 교황식 선거(Conclave)에서 의외의 인물이 당선될 확률은 얼마인가? ·················· 51
1.12 두 확률변수의 합과 곱 중에서 어느 것이 클까? ···················································· 59
1.13 어떤 방법이 정사각형의 면적을 정확하게 측정하는가? ········································· 65
1.14 두 수컷 호랑이의 평균 거리는 얼마쯤 되겠는가? ·················································· 69
1.15 최고 점수를 얻는 학생 수는 몇 명이 되겠는가? ···················································· 77
1.16 선거개표에서 항상 앞설 확률은 얼마인가? (Ballot problems) ········································································································ 82
1.17 호수에 사는 물고기 수를 어떻게 추정할 것인가? (Capture and recapture problems) ········································································· 87
1.18 모든 인형을 모으려면 몇 세트의 햄버거를 구입해야 하는가? (Coupon collection problems) ·················································································· 94
1.19 작품의 저자를 어떻게 파악할 것인가? ·································································· 100
1.20 편지와 편지봉투의 짝이 맞는 것은 몇 개가 될까? (Matching problems) ······························································································· 107
1.21 룸메이트를 구성할 때 신입생만으로 배정되지 않은 방은 몇 개가 되겠는가? ·· 113
1.22 성냥갑에 남아 있는 성냥은 몇 개일까? (Banach’s match box problems) ·········································································· 118

제2장 게임과 확률 문제
2.1 상금을 어떻게 분배할 것인가? ··············································································· 126
2.2 코리언 시리즈는 7차전까지 갈 것인가? ································································ 131
2.3 번트 사인을 내려야 하는가? ··················································································· 137
2.4 테니스 시합에서 이길 확률은 얼마인가? ······························································· 141
2.5 윷놀이가 보다 바람직한 게임이 되려면 어떻게 해야 할까? ······························· 146
2.6 주사위를 이용한 크랩(Crap) 게임의 승률은 얼마나 될까? ·································· 155
2.7 카지노 게임의 승률은 얼마나 될까? ······································································ 163
2.8 Parrondo의 역설은 역설인가? ················································································ 176
2.9 두 사람이 교대로 주사위 던지기 게임을 할 때 누가 이길까? ··························· 184
2.10 도박사가 큰돈을 벌 수 있을까? (Gambler’s ruin problems) ····························· 190
2.11 세배 봉투를 바꾸어야 하는가? ··············································································· 196
2.12 점심 내기에서 이길 확률은 얼마인가? ·································································· 202
2.13 몇 개의 주사위를 한꺼번에 던지는 것이 가장 유리한가? ··································· 205
2.14 연속경기 기록 달성이 얼마나 대단한가? ······························································· 208
2.15 상트페테르부르크 역설은 어떻게 설명할 수 있는가? ··········································· 212

제3장 최적 전략과 확률 문제
3.1 처음 한 선택을 바꾸어야 하는가? (Quiz show problems) ···························································································· 220
3.2 최고상을 획득하기 위한 좋은 전략은 무엇인가? (Best prize problems) ··········· 227
3.3 혈액을 혼합하여 검사하면 얼마나 효율적인가? (Group testing problems) ······················································································· 234
3.4 어떻게 위조 동전을 찾아 낼 수 있을까? ······························································ 240
3.5 시험점수를 올릴 수 있는 전략은 무엇일까? ························································· 248
3.6 교통경찰은 어떤 순찰 전략을 선택하는 것이 좋을까? ········································· 254
3.7 항공회사는 어느 정도 초과예약을 받는 것이 최적일까? ····································· 261
3.8 충전공정에서 평균을 어느 정도로 하는 것이 최적일까? (Canning problems) ································································································· 266
3.9 징검다리를 어떻게 설계하는 것이 좋을까? (Optimal arrangement problems in consecutive  out of  systems) ·········· 273
3.10 불량품 확인을 위한 최적의 검사방법은 무엇인가? (Inspection problems) ······························································································ 277
3.11 변동이 큰 두 부품을 어떻게 분류하여 조립하는 것이 좋은가? (Selective assembly problems) ·············································································· 283
3.12 책을 몇 번 교정하는 것이 최적일까? (Proofreading problems) ························································································· 290
3.13 소화기를 어떤 주기로 검사하는 것이 좋을까? (소화기 검사문제) ····································································································· 294
3.14 치킨 판매를 위해 준비해야 하는 최적의 공급량은 얼마일까? (최적 공급량 문제) ··································································································· 299
3.15 비 오는 날에는 어떤 코스로 출근해야 하는가? ··················································· 303
3.16 책들은 어떻게 정리하는 것이 검색에 유리한가? (List problems) ········································································································· 308
3.17 비를 맞지 않으려면 몇 개의 우산이 필요한가? ··················································· 314

제4장 기타 확률응용문제(Miscellaneous)
4.1 변동을 관리하기 위한 효율적인 방법은? (Control charts) ········································································································ 324
4.2 관리도에서 표본의 크기를 얼마로 하는 것이 좋은가? ········································· 329
4.3 크기가 큰 로트에서 얼마를 샘플링하는 것이 좋을까? (샘플링검사, Sampling inspection) ········································································· 334
4.4 Benford의 법칙은 존재하는가? ··············································································· 339
4.5 최대 몇 마리를 먹을 수 있는가? ··········································································· 345
4.6 시스템을 구성하는 부품 중 어떤 것이 중요한가? (중요도지수, 위원회 영향력(Power) 지수) ······························································ 349
4.7 정보를 구입하는 데 적정한 대가는 어느 정도인가? (Information values) ································································································· 353
4.8 왕따 참새는 몇 마리일까? ······················································································ 358
4.9 어떤 패턴이 더 자주 일어날까? ············································································· 365
4.10 버스를 기다리는 시간은 얼마나 될까? ·································································· 369
4.11 어떻게 중복해야 아이템의 신뢰도를 높일 수 있을까? ········································· 374
4.12 원주율을 어떤 방법으로 쉽게 확인할 수 있을까? ················································ 382
4.13 파레토(Pareto) 원리와 지니(Gini) 계수는 어떤 관계를 가지고 있는가? ·············· 391
4.14 오늘 2만보 이상 걸을 확률은 얼마인가? ······························································ 399
4.15 설문조사 결과에서 실제 음주운전 경험자의 비율은 얼마나 되겠는가? ············· 405
4.16 웹상에서 구매 요청이 하나도 없는 광고 수는 얼마나 될까? ····························· 410

∙ 참고문헌 ························································································································· 415
∙ 부록 ······························································································································· 425
∙ 찾아보기 ························································································································· 431
수학사 [경문수학산책 04]
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위상수학기초론
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실해석학 개론(2판)
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