In probability, what does the symbol $\cup$ (an upside-down U) between events $A$ and $B$ represent?

• A. Conditional probability of $A$ given $B$, i.e., $P\left(A\right|B)$
• B. The union of events: outcomes in $A$ or $B$ (or both), i.e., $A\cup B$
• C. The complement of an event: outcomes not in $A$, i.e., $A^c$
• D. The intersection of events: outcomes in both $A$ and $B$, i.e., $A\cap B$

Answer: (B)

Verified step by step guidance

1. Identify the symbol in question: the upside-down U symbol is written as \(\cap\) in LaTeX and represents a specific operation between two events \(A\) and \(B\) in probability.
2. Recall the meaning of common set operations in probability: the union \(A \cup B\) represents outcomes in \(A\) or \(B\) (or both), the complement \(A^c\) represents outcomes not in \(A\), and the intersection \(A \cap B\) represents outcomes common to both \(A\) and \(B\).
3. Understand that the upside-down U symbol \(\cap\) specifically denotes the intersection of two events, meaning the set of outcomes that are in both \(A\) and \(B\) simultaneously.
4. Express this formally as \(A \cap B\), which is the event containing all outcomes that belong to both \(A\) and \(B\) at the same time.
5. Therefore, the symbol \(\cap\) between events \(A\) and \(B\) represents the intersection of events, not the union, complement, or conditional probability.