You are conducting a controlled experiment where you have a single cell. After a certain and reoccurring amount of time, the cell has a 2/5 chance of dying, 2/5 chance of being idle, and a 1/5 chance of replicating. After a replication, each cell has the same amount of probability.
Given 1 million trials, what is the maximum number of cells produced?
I routinely get around 75 cells produced, given 1 million trials.
The probability of a trial creating 10 or more cells is only 2%. Given the chart below, you can see how the probability dramatically decreases once the trial begins.
import random import matplotlib.pyplot as plt import pandas as pd result =  for _ in range(1_000_000): cell =  cell.append(True) while True in cell: for x in range(len(cell)): random_num = random.randint(1,5) if cell[x] == True and random_num in (4,5): cell[x] = False elif cell[x] == True and random_num == 3: cell.append(True) result.append(len(cell)) print(max(result)) df = pd.Series(result) df = df.value_counts() plt.plot(df.index, df.values) plt.title('Distribution of Cell Count') plt.xlabel('Cell Count') plt.ylabel('Frequency') plt.show()