P(A) = 5/9 and P(B^c) = 5/11 (so P(B) = 6/11). Assuming A and B are independent, what is the probability that at least one of A or B occurs?

Introduction / Context:
The probability that at least one of two events occurs is given by P(A ∪ B) = P(A) + P(B) − P(A ∩ B). If independence is assumed, then P(A ∩ B) = P(A)P(B). This question provides P(A) and P(B^c).

Given Data / Assumptions:

• P(A) = 5/9.
• P(B^c) = 5/11, hence P(B) = 1 − 5/11 = 6/11.
• A and B are independent (stated in the title; needed to determine P(A ∩ B)).

Concept / Approach:
Use the union formula with independence: P(A ∪ B) = P(A) + P(B) − P(A)P(B). Compute exactly as a rational number to avoid rounding.

Step-by-Step Solution:

Verification / Alternative check:
Compute P(neither) = P(A^c)P(B^c) = (4/9)(5/11) = 20/99. Then 1 − 20/99 = 79/99, confirming the result.

Why Other Options Are Wrong:
6/11 and 5/9 are individual event probabilities, not the union. 4/9 is P(A^c). 0.8 is a rounded approximation (79/99 ≈ 0.79798) and is not exact.

Common Pitfalls:
Forgetting to subtract the intersection or neglecting the independence assumption; adding probabilities directly can exceed 1.

Final Answer:
79/99