#004easyProbability
Birthday Collision
Time Limit: 2sMemory: 256MB
Problem
Given n people in a room, compute the probability that at least two of them share the same birthday.
Assume 365 equally likely birthdays (no leap years) and that birthdays are independent.
This is a classic result from probability theory and appears frequently in quant interviews as a warm-up to understanding the birthday paradox — the counterintuitive result that the probability exceeds 50% with only 23 people.
Input Format
A single integer n — the number of people.
Output Format
The probability rounded to 4 decimal places.
Examples
Example 1
Input(A single integer n — the number of people.)
23
Output
0.5073
With 23 people, the probability of a shared birthday first exceeds 50%.
Example 2
Input(A single integer n — the number of people.)
1
Output
0.0000
A single person cannot share a birthday with anyone.
Constraints
- •1 ≤ n ≤ 365
- •Output rounded to 4 decimal places
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