The student's question revolves around probability calculations involving Boolean operators like 'AND' and 'OR' to determine the combined probabilities and whether events are 'mutually exclusive'. The 'AND Event' requires outcomes existing in both events, while 'OR' calculations combine probabilities of each event distinctly.
The student's question seems to be related to the concept of probability and the use of Boolean operators. Specifically, the terms 'AND', 'OR', and 'mutually exclusive' are key in understanding how to calculate combined probabilities for different events. When the question asks for the probability of G AND E, we're seeking the probability that both events G and E occur simultaneously. AND Event in probability implies that you are looking for outcomes that are common to both sets, which affects the calculation of their combined probability.
If the probability of G AND E is 0, it means that G and E are mutually exclusive; they cannot both occur at the same time. On the other hand, the use of 'OR' in probability refers to scenarios where at least one event must occur, but it's not required that both occur, which broadens the pool of possible outcomes. Therefore, when calculating P(G OR E), we would combine the probabilities of each event, taking care not to double-count any shared outcomes.
As for the query about mutual exclusivity justified numerically, if the events G and E are mutually exclusive, their intersection (G AND E) would be empty, and P(G AND E) would be 0. This numeric justification would show that the occurrence of one event precludes the occurrence of the other. To conclusively state if G and E are mutually exclusive, we need to know their individual probabilities and the probability of their intersection.