集合引用set()出现AttributeError:'NoneType' object has no attribute 'add'

import random
def birth():
    month=random.randint(1,12)
    if month==[1,3,5,7,8,10,12]:
        date=random.randint(1,31)
    elif month==2:
        date=random.randint(1,28)
    else:
        date=random.randint(1,30)
    birthday=(month+0.01*date)
    return birthday

counts=0
for frequence in range(100000):
    box=set()
    for i in range(23):
        box=box.add('birth()')
    if len(box)!=23:
        counts+=1

print('{:.5%}'.format(counts/100000))

Traceback (most recent call last):
File "C:\Users\lenovo\Desktop\python\Unit6.py", line 18, in
box=box.add('birth()')
AttributeError: 'NoneType' object has no attribute 'add'

你这目的是啥呢？