N Students

Few companies ask the below brain teaser to the candidates during the interview.

There are 40 students in the class. What is the possibility that at least 2 students share the same day of birth?

But what if it is a coding challenge:

There are N students in the class. What is the possibility that at least 2 students share the same day of birth? (Provided condition: No student is born in a leap year.)

Write a code that calculates the required probability.

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Solution:

General Formula:

Required probability = 1 – ( 365! / ((365-N)! * 365^N ))

Where N = Number of students in a class

Coding Solution:

# N Number of Students in Class
N = int (input('Enter Number of Students(N):')) 
mul1 = 1
for x in range(365-N+1,366):
    mul1 = mul1 * x

base = 365
exponent = N
mul2 = pow(base, exponent)
print('Probability of any two share same birthday:',1-(mul1/mul2))

Note : (Keeping non-coder readers in mind, code optimization is not fully utilized.)

Test Output 1:
Enter Number of Students(N):40
Probability of any two share same birthday: 89.1231809817949 %

Test Output 2:
Enter Number of Students(N):100
Probability of any two share same birthday: 99.99996927510722 %