Python Puzzles
Your All-Star baseball pitcher has a 15% chance of pitching a complete game. After how many starts does the pitcher have a 90% chance of pitching a complete game?
The pitcher has a 90% chance of pitching a complete game after 15 games. The average number of games to pitch a complete game is 6.7 games.
Here is the Python code to run the simulation.
import random import numpy as np # Set up the simulation parameters num_sims = 10000 # number of simulations to run comp_game_prob = 0.15 # probability of a complete game # Simulate the games and record the number of games until a complete game num_games_to_comp_game = [] for i in range(num_sims): num_games = 0 while True: num_games += 1 if random.random() <= comp_game_prob: num_games_to_comp_game.append(num_games) break # Calculate the 90th percentile percentile_90 = np.percentile(num_games_to_comp_game, 90) # Print the results print(f"Average number of games to a complete game: {sum(num_games_to_comp_game) / len(num_games_to_comp_game)}") print(f"Number of games at the 90th percentile: {percentile_90}")