Summary
The chapter covers using set operations in code to calculate intersections, unions, and exclusive regions of events and applies the inclusion-exclusion principle to compute and print probabilities.

General domain of usage
Probability theory

## Defining Sample Space and Events

```python
# Small numbers on a die
A = {1, 2, 3}

# Even numbers on a die  
B = {2, 4, 6}  

die_outcomes = 6
````

Here we define:

* $$A = \{1,2,3\}$$ representing "small" outcomes;
* $$B = \{2,4,6\}$$ representing "even" outcomes.

The total number of die outcomes is 6.

# Small numbers on a die
A = {1, 2, 3}
# Even numbers on a die  
B = {2, 4, 6}  
die_outcomes = 6

print(f'A and B = {A & B}')  # {2}
print(f'A or B = {A | B}')   # {1, 2, 3, 4, 6}

* The **intersection** $$A \cap B = \{2\}$$ → common element.
* The **union** $$A \cup B = \{1,2,3,4,6\}$$ → all elements in A or B.

# Small numbers on a die
A = {1, 2, 3}
# Even numbers on a die  
B = {2, 4, 6}  
die_outcomes = 6

A_and_B = A & B  # {2}
A_or_B = A | B   # {1, 2, 3, 4, 6}

P_A = len(A) / die_outcomes
P_B = len(B) / die_outcomes
P_A_and_B = len(A_and_B) / die_outcomes
P_A_or_B = P_A + P_B - P_A_and_B

print("P(A) =", P_A)
print("P(B) =", P_B)
print("P(A ∩ B) =", P_A_and_B)
print("P(A ∪ B) =", P_A_or_B)

We use the formulas:

* $$P(A) = \frac{\raisebox{1pt}{$|A|$}}{\raisebox{-1pt}{$6$}} = \frac{\raisebox{1pt}{$3$}}{\raisebox{-1pt}{$6$}}$$;
* $$P(B) = \frac{\raisebox{1pt}{$|B|$}}{\raisebox{-1pt}{$6$}} = \frac{\raisebox{1pt}{$3$}}{\raisebox{-1pt}{$6$}}$$;
* $$P(A \cap B) = \frac{\raisebox{1pt}{$|A \cap B|$}}{\raisebox{-1pt}{$6$}} = \frac{\raisebox{1pt}{$1$}}{\raisebox{-1pt}{$6$}}$$;
* $$P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{\raisebox{1pt}{$5$}}{\raisebox{-1pt}{$6$}}$$.

only_A = A - B   # {1, 3}
only_B = B - A   # {4, 6}

print(only_A)
print(only_B)

* Elements only in A: {1, 3};
* Elements only in B: {4, 6}.

This course distills the essentials of Python's math module, focusing on trigonometric functions, logarithmic operations, and mathematical constants. Learners will gain hands-on experience using Python to perform these standard mathematical computations, ideal for beginners seeking practical skills with the math module.

Implementing Probability Basics in Python

Defining Sample Space and Events

Performing Set Operations

Calculating Probabilities

Additional Set Details