Solution

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If a classifier makes each of its predictions entirely at random, choosing each predicted label to be \(0 \) or \(1 \) with equal probability, then its probability of misclassifying any given example will be exactly \( \frac{1}{2} \) . Therefore, the error of this classifier will always be \( \frac{1}{2} \) , regardless of the data on which the error is measured.