import pandas as pd
import numpy as np

df = pd.read_csv('superstore_sales.csv')
print(df.shape)
print(df.head(3))

total_orders = len(df)
tech_orders = (df['Category'] == 'Technology').sum()
p_tech = tech_orders / total_orders
print(f'Real orders: {total_orders}')
print(f'Real Technology orders: {tech_orders}')
print(f'P(Technology) = {p_tech:.4f}')

category_probs = df['Category'].value_counts(normalize=True)
print(category_probs)
print(f'Real probabilities sum to: {category_probs.sum():.4f}')

p_not_tech = 1 - p_tech
check = (df['Category'] != 'Technology').mean()
print(f'P(not Technology) via complement rule: {p_not_tech:.4f}')
print(f'P(not Technology) computed directly: {check:.4f}')

p_furniture = (df['Category'] == 'Furniture').mean()
p_tech_or_furniture = p_tech + p_furniture
check_or = df['Category'].isin(['Technology', 'Furniture']).mean()
print(f'P(Technology) + P(Furniture) = {p_tech_or_furniture:.4f}')
print(f'P(Technology or Furniture) direct = {check_or:.4f}')

p_tech2 = (df['Category'] == 'Technology').mean()
p_west = (df['Region'] == 'West').mean()
p_tech_and_west = ((df['Category'] == 'Technology') & (df['Region'] == 'West')).mean()
p_tech_or_west = p_tech2 + p_west - p_tech_and_west
check_or2 = ((df['Category'] == 'Technology') | (df['Region'] == 'West')).mean()
print(f'P(Technology or West) via full rule: {p_tech_or_west:.4f}')
print(f'P(Technology or West) direct: {check_or2:.4f}')

p_tech_given_west = df.loc[df['Region'] == 'West', 'Category'].eq('Technology').mean()
p_tech_overall = (df['Category'] == 'Technology').mean()
print(f'P(Technology | West) = {p_tech_given_west:.4f}')
print(f'P(Technology) overall = {p_tech_overall:.4f}')

p_a_and_b = p_tech_and_west
p_b = p_west
p_a_given_b = p_a_and_b / p_b
print(f'P(Technology | West) via definition: {p_a_given_b:.4f}')
print(f'Matches direct calculation: {abs(p_a_given_b - p_tech_given_west) < 1e-9}')

region_category = pd.crosstab(df['Region'], df['Category'], normalize='index')
print(region_category.round(4))

rng = np.random.default_rng(seed=42)
coin_flips = rng.integers(0, 2, size=10000)
p_heads = coin_flips.mean()
print(f'Simulated P(heads) over 10,000 flips: {p_heads:.4f}')

sampled_orders = rng.choice(df['Category'], size=5000, replace=True)
sampled_probs = pd.Series(sampled_orders).value_counts(normalize=True)
print('Simulated by resampling from the real category distribution:')
print(sampled_probs)
print()
print('Original real distribution:')
print(category_probs)

import matplotlib.pyplot as plt

sample_sizes = np.arange(10, 5001, 10)
running_flips = rng.integers(0, 2, size=5000)
running_means = np.cumsum(running_flips) / np.arange(1, 5001)
plt.figure(figsize=(9, 4))
plt.plot(running_means, color='steelblue', linewidth=1)
plt.axhline(0.5, color='darkred', linestyle='--', label='True probability (0.5)')
plt.title('Simulated Coin Flip Probability Converging with Sample Size')
plt.xlabel('Number of Flips')
plt.ylabel('Running Probability of Heads')
plt.legend()
plt.show()

for n in [10, 100, 1000, 5000]:
    est = running_means[n - 1]
    print(f'After {n} flips: estimated P(heads) = {est:.4f}, error = {abs(est - 0.5):.4f}')