Probability Axioms & Addition Rule

Kolmogorov's Axioms

Every probability measure $P$ must satisfy three axioms:

1. Non-negativity: $P(A) \geq 0$ for all events $A$
2. Normalization: $P(\Omega) = 1$
3. Countable additivity: if $A \cap B = \emptyset$, then $P(A \cup B) = P(A) + P(B)$

These three axioms are all you need to derive all of probability theory.

The Addition Rule

For any two events (not necessarily disjoint):

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

The $P(A \cap B)$ term corrects for double-counting outcomes in both $A$ and $B$.

# Drawing a card: P(heart or face card)
p_heart = 13/52       # P(A)
p_face  = 12/52       # P(B)
p_both  = 3/52        # P(A ∩ B): face cards that are hearts

p_union = p_heart + p_face - p_both
print(round(p_union, 4))  # 0.4231

Mutually exclusive events ($A \cap B = \emptyset$) simplify to $P(A \cup B) = P(A) + P(B)$.

Your Task

Implement union_probability(p_a, p_b, p_ab) that returns $P(A \cup B)$, rounded to 4 decimal places.