我有两件互相独立的装备，分别可以增加我百分之9和百分之13的暴击几率，那么，我现在攻击两次，两次攻击...

問題

我有两件互相独立的装备，分别可以增加我百分之9和百分之13的暴击几率，那么，我现在攻击两次，两次攻击至少有一次暴击的概率是多少

思考

Breaking down the problem

I’m clarifying the probabilities of critical hits from two pieces of equipment, each with a 9% and 13% chance, respectively. This leads me to calculate the combined probability for two attacks with at least one critical hit.

Combining probabilities

I’m adding the independent critical hit rates from two pieces of equipment: 9% and 13%. Then, I’m calculating the combined critical hit probability and the chance of at least one critical hit in two attacks.

Calculating critical hit odds

OK, let me see. Amplifying the collision likelihood from each equipment piece, factoring in independence, and then determining the chance of at least one critical hit across two attacks.

Figuring out the odds

First, I’m figuring out a single attack's 20.83% critical hit chance. Then, for two attacks, reducing to around 37.32%. This showcases progress and potential areas for enhancement.

Thought for 2m 7s

回答

先说明一下思路：如果有两件装备，分别独立提供 9% 和 13% 的暴击几率，那么单次攻击触发暴击的概率并不是简单的 9% + 13%，而是按照“独立判定、不冲突”的方式计算。具体步骤如下：

计算单次攻击的暴击率
- 先计算“都不暴击”的概率： $P(\text{都不暴击}) = (1 - 0.09)\times (1 - 0.13) = 0.91 \times 0.87 = 0.7917$
- 那么“至少有一次暴击”（也就是最终暴击成功）的概率即为： $P(\text{暴击}) = 1 - P(\text{都不暴击}) = 1 - 0.7917 = 0.2083$
因此，单次攻击的暴击率为约 20.83%。
攻击两次，至少有一次暴击的概率
- 令单次攻击的暴击率为 $p = 0.2083$ ，则两次攻击都不暴击的概率为： $(1 - p)^2 = 0.7917^2 \approx 0.6268$
- 所以两次攻击“至少有一次暴击”的概率为： $1 - (1 - p)^2 = 1 - 0.6268 = 0.3732$
换算成百分比，大约是 37.32%。

结论：
当每次攻击的暴击率由 9% 和 13% 两件独立装备共同叠加后，单次攻击的暴击率约为 20.83%；若连续攻击两次，则两次攻击中至少出现一次暴击的概率大约 37.32%。

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