Probability And Expectation: In Mathematical Olympiad And Competitions

by Zun Shan, Shanping Wang (Translator)

Overview

In China, lots of excellent students who are good at maths take an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year.The author is one of the senior coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. This book will, in an interesting problem-solving way, explain what probability theory is: its concepts, methods and meanings; particularly, two important concepts — probability and mathematical expectation (briefly expectation) — are emphasized. It consists of 65 problems, appended by 107 exercises and their answers.

Product Details

ISBN-13:	9789813141490
Publisher:	World Scientific / East China Normal Univ Press, China
Publication date:	09/06/2016
Series:	Mathematical Olympiad Series , #14
Pages:	208
Product dimensions:	5.90(w) x 9.00(h) x 0.60(d)

Table of Contents

Introduction v

0 Basic Knowledge 1

1 Coin Tossing 5

2 General Di Qing's Coins 8

3 Rolling Dice 11

4 Wei Xiao-bao's Bet 13

5 Hold All the Trump Cards 16

6 Roll One-Spot 18

7 Red Balls and Black Balls 20

8 Same Month and Day 23

9 Integer Divisibility 26

10 Repeated Experiments 28

11 Silver Medal Dream 30

12 Fight Between Brothers 32

13 Subject Groups 34

14 More Dice 36

15 Custodian Turned Thief 38

16 Put Back or Not 40

17 Match Problem 43

18 Put Balls into Drawers 45

19 Problem of Matches 47

20 Trial in a Three-Judge Court 49

21 Win Twice in Succession 51

22 Fire Blank Shots 54

23 Catch a Turtle in a Jar 56

24 Diagnosis Rate 58

25 Running Well 60

26 Money Change Problem 62

27 Donkey versus Elephant 64

28 East Wind versus West Wind 67

29 Dowry Problem (I) 69

30 Dowry Problem (II) 72

31 Job Interview 75

32 Boxing Match (I) 78

33 Boxing Match (II) 81

34 Boxing Match (III) 84

35 Rein in on the Brink of the Precipice (I) 88

36 Rein in on the Brink of the Precipice (II) 91

37 Who Will Gamble Away? 92

38 Equal in Strength 94

39 Put All Money in One Bet 96

40 Indeterminate Equation 97

41 Throw Copper Coin onto a Small Table 99

42 Appointment of People in Hurry 101

43 Obtuse Triangle 103

44 Buffon's Needle 105

45 Bertrand's Paradox 108

45 Odd or Even Number 112

47 Rational or Irrational Number 114

48 Real Roots or Not 116

49 Divide the Stake 119

50 Sleeping Beauty 122

51 Number of Hits 124

52 The Suicide Club 126

53 The First Ace 128

54 How Many Pairs in Average 130

55 Many Holidays 132

56 Buy Lottery Tickets 134

57 Not to Indulge in Gambling 136

58 Social Party 138

59 Success by Trying Once or More Times 139

60 The 108 Heroes 141

61 Who is Sick? 143

62 A Fallen and Broken Rod 145

63 Broken into Three Fragments 146

64 The Number of Cross Points 149

65 Throw a Wire Ring 151

Exercises 153

Key to Exercises 169