猜拳（石头剪刀布）公平吗？
Is rock-paper-scissors fair?
三种出法互相克制，谁也没有永远赢的办法，所以大致公平。它靠的是随机出拳，而不是力气大小。
The three moves beat each other in a loop, so no choice always wins, making it roughly fair. It relies on random choices, not on strength.
难度 入门 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
美国数学会(AMS)《博弈论与经济模型》
American Mathematical Society (AMS), Game Theory and Economic Modeling
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787100047876（豆瓣书目条目: 博弈论与经济模型）
#公平 #随机
为什么天气预报说“有雨的概率”？
Why does weather say “chance of rain”?
天气受很多因素影响，没法百分之百确定。科学家算出一个可能性，比如60%会下雨，帮我们决定带不带伞。
Weather depends on many factors and cannot be 100% certain. Scientists work out a likelihood, like a 60% chance of rain, to help us decide on an umbrella.
难度 入门 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#概率 #天气
为什么电脑用“是”和“否”来思考？
Why do computers think in “yes” and “no”?
电脑用二进制，只认0和1，就像回答“是”或“否”。把很多个对错叠起来，就能算出复杂的问题。
Computers use binary, recognizing only 0 and 1, like answering yes or no. Stacking many right-or-wrong answers lets them solve hard problems.
难度 入门 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#二进制 #逻辑
什么是“可能”“一定”“不可能”？
What are “maybe,” “certain,” and “impossible”?
“一定”是肯定会发生，比如太阳会升起。“可能”是也许会，“不可能”是绝对不会，比如太阳从西边出来。
“Certain” means it will surely happen, like the Sun rising. “Maybe” means it might, and “impossible” means it never will, like the Sun rising in the west.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
《概率论与数理统计》
Probability Theory and Mathematical Statistics (《概率论与数理统计》)
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787312018381（豆瓣书目条目: 概率论与数理统计）
#概率 #可能
为什么抽奖不一定中奖？
Why don't we always win a lottery?
中奖的号码只是很多可能里的一个，抽中的机会很小。大多数时候抽到的是别的号码，所以不中很正常。
The winning number is just one of many possibilities, so the chance of hitting it is small. Most times another number is drawn, so not winning is normal.
难度 入门 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
Grinstead, C. M. 与 Snell, J. L., 《概率导论》, 美国数学会 (AMS)
Grinstead, C. M. & Snell, J. L., 'Introduction to Probability', American Mathematical Society
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780821807491 (1997)
#抽奖 #概率
什么是“平均数”，它想告诉我们什么？
What is an “average” and what does it tell us?
平均数把一堆数加起来再均分成几份，代表一个“中间水平”。但它会盖住特别大或特别小的个别情况。
An average adds a bunch of numbers and splits them evenly, standing for a middle level. But it hides especially big or small individual cases.
难度 入门 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
《概率论与数理统计》
Probability Theory and Mathematical Statistics (《概率论与数理统计》)
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787312018381（豆瓣书目条目: 概率论与数理统计）
#平均数 #统计
为什么掷骰子能用来玩游戏？
Why can we use dice to play games?
骰子每一面朝上的机会一样，所以谁也猜不准会掷出几。这种“公平的不确定”让游戏变得又紧张又好玩。
Each face of a die has the same chance to land up, so no one can guess the number. This fair uncertainty makes games exciting and fun.
难度 入门 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
Grinstead, C. M. 与 Snell, J. L., 《概率导论》, 美国数学会 (AMS)
Grinstead, C. M. & Snell, J. L., 'Introduction to Probability', American Mathematical Society
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780821807491 (1997)
#骰子 #公平
抛硬币为什么有时正面、有时反面？
Why does a coin sometimes land heads and sometimes tails?
硬币两面差不多重，抛起来落哪面全看运气。所以正反面都有机会出现，谁也不能保证一定是哪面。
A coin's two sides weigh about the same, so which way it lands is luck. Both sides have a chance, and no one can be sure which will show.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
Grinstead, C. M. 与 Snell, J. L., 《概率导论》, 美国数学会 (AMS)
Grinstead, C. M. & Snell, J. L., 'Introduction to Probability', American Mathematical Society
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780821807491 (1997)
#硬币 #运气
猜拳输了为什么不算不公平？
Why is losing rock-paper-scissors not unfair?
因为谁输谁赢全靠随机出拳，不是力气大就赢。大家机会一样，所以输了也只是运气。
Winning or losing depends on random choices, not on who is stronger. Everyone has the same chance, so losing is just luck.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录含书名，但缺版次 / 出版社 / 年份中的一部分，需编辑补全后才能做独立比对。
J. Li, F. Qi 与 Y. Ma《Influences of Previous Outcomes and the Players' Skill on the Behavior in the Iterated Rock-Paper-Scissors Game》, PLOS ONE 9(8):e105293, 2014
J. Li, F. Qi & Y. Ma, 'Influences of Previous Outcomes and the Players' Skill on the Behavior in the Iterated Rock-Paper-Scissors Game', PLOS ONE 9(8):e105293, 2014
#公平 #随机
什么是质数，它能帮我们做什么？
What are prime numbers and what are they good for?
质数只能被1和自己整除，像2、3、5、7。今天电脑用很大的质数来给秘密信息上锁，保护我们的聊天和付款。
Prime numbers divide only by 1 and themselves, like 2, 3, 5, 7. Today computers use huge primes to lock secret messages and protect our chats and payments.
难度 入门 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
K. H. Rosen《Elementary Number Theory and Its Applications》（第6版），Pearson，2011，§6.2
K. H. Rosen, Elementary Number Theory and Its Applications, 6th ed., Pearson, 2011, §6.2
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780321717757 (2011)
#质数 #密码