What is the sum of the probabilities p(G | E) and p(I | E)?

The sum of the probabilities p(G | E) and p(I | E) being equal to 1 indicates that G and I are mutually exclusive events under the condition E. In probability theory, when two events cannot occur at the same time (mutually exclusive), the sum of their probabilities equals 1 if they encompass all possible outcomes of the condition E.

For example, if E represents a scenario where either G or I must occur, the probabilities of these outcomes directly reflect that constraint. Thus, if you have two outcomes that are exclusive (only one of them can happen given E), their probabilities combined should sum to 1, confirming that they fully represent all the possibilities that could happen in that context.

This principle is fundamental in probability and is commonly applied in determining outcomes in various situations, which is critical for a forensic analyst when evaluating evidence or interpreting data from an investigation.