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Question
the word or in probability implies that we use the rule
Brief Explanations
In probability, the word "or" indicates that we are dealing with the union of events. The Addition Rule in probability is used to calculate the probability of the union of two events. For two events \(A\) and \(B\), the formula for the Addition Rule is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). This rule accounts for the possibility of overlapping events (the \(P(A\cap B)\) term). The other options:
- The Empirical Rule is related to the normal distribution (e.g., about 68 - 95 - 99.7% of data within 1, 2, 3 standard deviations).
- The Combination Rule is used for counting the number of ways to choose \(k\) elements from \(n\) elements (\(C(n,k)=\frac{n!}{k!(n - k)!}\)).
- The Large Numbers Rule (Law of Large Numbers) states that as the number of trials increases, the sample mean approaches the population mean.
- The Multiplication Rule (\(P(A\cap B)=P(A)\times P(B|A)\) or \(P(A)\times P(B)\) for independent events) is for the intersection of events.
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Addition