91Ó°ÊÓ

In probability theory, the union of events refers to a scenario where at least one of the given events occurs. For instance, if we have two events, like visiting Beijing or Xi'an, the union is the chance of visiting at least one of these places. The union is represented by the mathematical symbol \( \cup \), which means "or" in this context. The formula to calculate the probability of the union of two events, say \( A \) and \( B \), is \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \). This formula subtracts the overlap because adding \( P(A) \) and \( P(B) \) counts it twice. This concept helps us understand overlapping probabilities by ensuring we don't "double count" the tourists visiting both Beijing and Xi'an.

Conditional probability is the likelihood of an event occurring given that another event has already happened. Although not directly heavy-weighted in this exercise, it supports our understanding of probability relationships.Imagine two interconnected events: visiting Beijing and Xi'an. Knowing one has occurred can change the likelihood of the other. This is mathematically represented as \( P(A | B) \), meaning the probability of \( A \) occurring given that \( B \) occurred.Understanding this concept helps uncover dependencies between events. Even if we don't utilize it directly, recognizing how events might overlap or influence one another can clarify union calculations.

Arithmetic calculations are crucial for resolving probability exercises. In our example, we used basic arithmetic operations to find the probability of a tourist visiting at least one of the places.Once we identified known probabilities: 0.60 for Beijing, 0.40 for Xi'an, and 0.30 for both, we employed the arithmetic inside the union formula. By substituting, \( 0.60 + 0.40 - 0.30 \), we achieved the final result of 0.70.Arithmetic is not just about numbers; it involves careful handling of data to reach logical conclusions. These simple calculations underscore the importance of arithmetic when addressing probability issues.