Final answer:
The missing reason in the 2-column proof could be any of the given properties of equality, depending on the specific steps taken in the proof. In the section about probabilities, mutual exclusivity of events G and E can be determined by checking if P(G AND E) is equal to 0.
Step-by-step explanation:
The missing reason in the 2-column proof provided may relate to properties of equality and algebraic operations which are generally asked in mathematical problems or proofs. In the context of the proof, options like Subtraction Property of Equality (POE), Multiplication POE, Addition POE, and Transitive Property are given. The correct answer depends on the statements given in the proof, which are not provided in the question. However, these properties are essential when transitioning from one step to another in a proof by justifying the algebraic manipulation of equations.
For example, Subtraction POE is used when both sides of an equation are subtracted by the same value, Multiplication POE when both sides are multiplied by the same value, Addition POE when both sides are added by the same value, and the Transitive Property is used when expressing equality between two entities by a common third entity. Without the specific statements of the proof, indicating which step was taken to reach the missing reason, it is not possible to determine the correct answer.
Concerning the question about probabilities, when asked about P(G), P(G|E), P(G AND E), P(G OR E), and whether G and E are mutually exclusive, these relate to the concepts of basic probability. Mutually exclusive events cannot happen at the same time. If numerical probabilities for G and E are provided, a justification can be given by checking if P(G AND E) equals 0, which is the case when events G and E are mutually exclusive.