birthday.ipynb

Kernel: Python 2 (SageMath)

def birthday(n):
    if n == 0:
        return 0.
    l = birthday(n-1)
    return l + (1-l)*(n-1)/365.

birthday(1)

0.0

birthday(2)

0.0027397260273972603

birthday(17)

0.31500766529656066

birthday(22)

0.4756953076625501

birthday(23)

0.5072972343239854

birthday(30)

0.7063162427192686

birthday(365)

1.0