main.py

import random

probs = [1.2, 1.2, 1.1, 1.05, 1.5, 1.75, 2.0, 1.7]
probs.append(100 - sum(probs))
populations = list(range(len(probs)))


def getTime():
    time = 0
    collected = [False for key in populations]
    while True:
        time += 1
        choice = random.choices(populations, weights=probs, k=1)[0]
        collected[choice] = True
        if sum(collected[:8]) >= 6:
            return time


ts = []
N = 100_000
for i in range(N):
    ts.append(getTime())
print(sum(ts) / N)