Which of the following is true regarding the relationship between p(G | E) and p(I | E)?

The correct assertion is that p(G | E) and p(I | E) must sum to 1, which reflects the fundamental principles of probability theory. When dealing with conditional probabilities, specifically when E represents a complete event or set of outcomes, the probabilities of all possible outcomes given E will always sum to 1. This is because E encompasses all scenarios in which the events G and I can occur.

If G and I represent mutually exclusive outcomes (meaning they cannot happen at the same time), then the probabilities of these events conditioned on E would indeed need to sum up to 1. For example, if you consider a standard example in probability where there are only two mutually exclusive outcomes, the sum of the probabilities of the occurrence of those outcomes must equal the total certainty, which is 1.

The other potential assertions do not hold in the context of probability. The idea that the probabilities might sum to infinity does not apply in probability theory, as all probabilities must fall within the range of 0 to 1. Independence of probabilities does not apply directly here unless specified, as the relationship defined by the condition E connects them. Finally, while they may exhibit some form of correlation or dependency, claiming direct proportionality without further context does not capture the