from random import sample
from collections import defaultdict

tests = 100000
population = range(25)

weeks = defaultdict(int)
for _ in range(tests):
    A = 25*[0]
    B = 25*[0]
    week = 0
    while sum(B)<25:
        sam = sample(population, 2)
        for s in sam:
            if A[s] == 0:
                A[s] = 1
            elif B[s] == 0:
                B[s] = 1
        week +=1
    weeks[week] += 1

expect = sum(k*weeks[k] for k in weeks)/tests
print(tests, 'trials')
print('Mean number of weeks', expect)
for n in range(50, 175, 25):
    p = sum(weeks[k] for k in weeks if k > n)/tests
    print('Prob of more than %d weeks: %s'%(n,p))

100000 trials
Mean number of weeks 70.20713
Prob of more than 50 weeks: 0.91649
Prob of more than 75 weeks: 0.3142
Prob of more than 100 weeks: 0.05515
Prob of more than 125 weeks: 0.00849
Prob of more than 150 weeks: 0.00133