🪙 抛硬币概率Coin Flip Probability
n 次中恰好 k 次正面：C(n,k) / 2^n（公平硬币）。本地处理。可设置「次数」、「正面次数」。Exactly k heads in n fair flips: C(n,k)/2^n. Processed locally. Settings: Flips, Heads.
使用说明与常见问题How-to & FAQ
「抛硬币概率」是什么？What is the Coin Flip Probability tool?
n 次中恰好 k 次正面：C(n,k) / 2^n（公平硬币）。本地处理。可设置「次数」、「正面次数」。Exactly k heads in n fair flips: C(n,k)/2^n. Processed locally. Settings: Flips, Heads.
如何使用「抛硬币概率」？How do I use the Coin Flip Probability tool?
在「抛硬币概率」中，填写「次数」、「正面次数」等参数，结果会随输入实时计算并显示在下方。In the Coin Flip Probability: Fill in "Flips", "Heads"; results are recalculated instantly as you type.
硬币不均匀可以吗？What about a biased coin?
不可以，本页只算公平硬币（p = 1/2）：恰好 k 次正面的概率 = C(n, k) ÷ 2ⁿ。不均匀硬币要用二项分布 C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ，可用二项分布计算器。No, this page assumes a fair coin (p = 1/2): P(exactly k heads) = C(n, k) ÷ 2ⁿ. A biased coin needs the binomial formula C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ, available in a binomial distribution tool.
能举个计算实例吗？Can you show a worked example?
例如在「抛硬币概率」中填 次数 = 10，正面次数 = 5，结果区显示：恰好 k 次概率：0.24609375；百分比：24.6094%For example, entering Flips = 10, Heads = 5 in the Coin Flip Probability gives: P(exactly k): 0.24609375; Percent: 24.6094%
哪些输入会被检查？Which inputs are validated?
「抛硬币概率」会检查这些输入——「次数」、「正面次数」：必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Coin Flip Probability checks its inputs — "Flips", "Heads": required; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「抛硬币概率」的设置：「次数」默认 10；「正面次数」默认 5。每次生成结果都按当前设置处理。Settings in the Coin Flip Probability — "Flips" default 10; "Heads" default 5. The result always uses the current settings.
计算精度如何？How precise are the results?
「抛硬币概率」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Coin Flip Probability uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「抛硬币概率」免费吗？需要注册吗？Is the Coin Flip Probability free? Do I need an account?
「抛硬币概率」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Coin Flip Probability is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.