MathProblem 37 Common birthday problem

标签：frac people 0.5 37 birthday MathProblem problem 365

What is the minimum number of people do you need, chosen at random, so that there is at least a 50% chance that at least two have the same birthday. Assume that people are born randomly throughout the year. You may ignore leap day.

Solution

假设一年有 365天，假设有 \(n\) 人。现要求至少有两个人有相同的生日。那么我们求其相反面：每个人生日都不同的概率：

\[P_1=\frac{365}{365}\cdot ...\cdot \frac{365-n+1}{365}=\prod_{i=0}^{n-1}\frac{365-i}{365} \]

所以答案就是：\(1-P_1\ge 0.5 \Rightarrow P_1\le 0.5\)
求解得到 \(n=23\)

标签：frac,people,0.5,37,birthday,MathProblem,problem,365
From： https://www.cnblogs.com/xinyu04/p/16593566.html