# import libraries for probability and data manipulation
import warnings; warnings.filterwarnings('ignore')
import numpy as np
import pandas as pd

# Simulate 10 coin flips
flips = np.random.choice(['Heads', 'Tails'], size=10)
print('Ten coin flips:', flips)

# Count heads and tails
unique, counts = np.unique(flips, return_counts=True)
results = dict(zip(unique, counts))
print('Counts:', results)

# Calculate probability of heads
prob_heads = results.get('Heads', 0) / len(flips)
print('Estimated probability of heads:', prob_heads)

# Data setup
import seaborn as sns
titanic = sns.load_dataset('titanic')
print('Shape:', titanic.shape)
titanic.head()

# Probability of survival overall
prob_survived = titanic['survived'].mean()
print('Probability any passenger survived:', prob_survived)

# Probability of survival, given the passenger was female
female = titanic[titanic['sex']=='female']
prob_survived_female = female['survived'].mean()
print('Probability of survival given female:', prob_survived_female)

# Probability of survival, given the passenger was male
male = titanic[titanic['sex']=='male']
prob_survived_male = male['survived'].mean()
print('Probability of survival given male:', prob_survived_male)

# Compare probabilities for different passenger classes
for pclass in [1,2,3]:
    class_group = titanic[titanic['pclass']==pclass]
    prob = class_group['survived'].mean()
    print(f'Survival chance in class {pclass}:', prob)
    

# Check independence by comparing probabilities
# If P(Survived|Female) = P(Survived), they are independent
print('P(Survived):', prob_survived)
print('P(Survived|Female):', prob_survived_female)
if np.isclose(prob_survived, prob_survived_female):
    print('Survival and being female are independent')
else:
    print('Survival and being female are not independent')
    

# Visualize survival by sex
import matplotlib.pyplot as plt
pd.crosstab(titanic['sex'], titanic['survived']).plot(kind='bar', stacked=True)
plt.xlabel('Sex')
plt.ylabel('Count')
plt.title('Titanic Survival by Sex')
plt.legend(['Did not survive', 'Survived'])
plt.show()

# Challenge! Type a name and see if you would survive, using real probabilities
name = input('Enter your first name: ')
sex = input('Are you male or female? ').strip().lower()
your_prob = prob_survived_female if sex=='female' else prob_survived_male
print(f'Hi {name.title()}, your chance of survival might have been:', your_prob)

# Simulate two dice rolls, test independence
die1 = np.random.randint(1,7, size=1000)
die2 = np.random.randint(1,7, size=1000)
event_A = die1 == 6
event_B = die2 == 6
P_A = np.mean(event_A)
P_B = np.mean(event_B)
P_AB = np.mean(event_A & event_B)
print('P(A):', P_A)
print('P(B):', P_B)
print('P(A and B):', P_AB)
print('If independent, P(A and B) should equal P(A)*P(B):', P_A * P_B)

# Challenge: What is the conditional probability a third class female survived?
third_females = titanic[(titanic['sex']=='female') & (titanic['pclass']==3)]
prob_third_female_survived = third_females['survived'].mean()
print('Chance a 3rd class female survived:', prob_third_female_survived)

# Experiment: What happens if we treat sex and class as independent?
P_class_3 = (titanic['pclass']==3).mean()
P_female = (titanic['sex']=='female').mean()
P_both_independent = P_class_3 * P_female
P_both_observed = ((titanic['pclass']==3) & (titanic['sex']=='female')).mean()
print('If independent, P(class 3 and female):', P_both_independent)
print('Observed P(class 3 and female):', P_both_observed)