In the Digital Communication lecture, information was described as the opposite of probability.

Question

BlackTom AI · Accepted Answer

The question states: 'In the Digital Communication lecture, information was described as the opposite of probability.'
Option 1: True. In information theory, there is a fundamental relationship between information content and probability: information (often quantified as self-information or surprisal) is defined as I(p) = -log2(p). This means that as probability p increases, information decreases, and as probability decreases (events are less likely), information increases. While some will phrase this as 'information is inversely related to probability' rather than the literal opposite, many pedagogical explanations describe information content as being conceptually opposite to probability in the sense of an inverse, or in terms of surprise vs. likelihood. Therefore, labeling the statement as True aligns with the intuition that information grows when events are unlikely, i.e., when probability is low.
Option 2: False. If one interprets 'opposite' strictly as a diametric, non-overlapping antonym, this is inaccurate because information and probability are not simple opposites; they are related measures, with information depending on probability. The common formal relation is inverse (or monotonic) rather than a direct opposite, so calling them exact opposites would be an oversimplification and not precise.
In summary, the claim hinges on whether the course framed information as inversely related to probability and described that relationship in terms of opposites or inverse relationship. Based on standard information theory, the information content decreases with high probability and increases with low probability, which supports the idea that information is conceptually opposite to probability in terms of behavior across the probability scale, hence True in this context.

In the Digital Communication lecture, information was described as the opposite of probability. 判断题

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