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Where ( P(x_i) ) is the probability of each possible outcome ( x_i ). Entropy encapsulates the average amount of information one might expect to gain by observing the outcome.
In essence, a fair coin has higher entropy than a biased coin because every outcome is equally probable, leading to maximum unpredictability and surprise.
Implications in Computer Science
Understanding entropy directly connects to practical computer science applications, such as data compression and error correction. By determining the entropy of a dataset, computer scientists can design optimal encoding schemes that minimize redundancy while preserving essential information.