Which of the Following Mathematical Expressions Represents the Sum Rule

question 62

Multiple Choice

Which of the following mathematical expressions represents the sum rule, which can be used to determine the probability of either event X or event Y occurring if they CANNOT occur simultaneously? (In the equations below, P_x means probability of event X; P_y means probability of event Y.)

• A) = (P_x)² + (P_y)²
• B) = P_x + P_y
• C) = P_xP_y
• D) = (P_x + P_y)²

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Definitions:

Prior Probabilities

The probabilities of events based on prior knowledge before any new evidence is considered.

Likelihood Probabilities

The probabilities that quantify the plausibility of different parameter values for a statistical model given the observed data.

Posterior Probabilities

The probabilities that are adjusted after taking into account known or observed evidence, particularly in the context of Bayesian inference.

Addition Rule

In probability theory, a rule that calculates the probability of either of two mutually exclusive events occurring.