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This paper considers the problem of fair probabilistic binary classification with binary protected groups. The classifier returns scores, and a practitioner predicts labels using a certain cut-off threshold based on the desired trade-off between false positives vs. false negatives. It derives these thresholds from the ROC of the classifier. The resultant classifier may be unfair to one of the two protected groups in the dataset. It is desirable that no matter what threshold the practitioner uses, the classifier should be fair to both the protected groups; that is, the $\mathcal{L}_p$ norm between FPRs and TPRs of both the protected groups should be at most $\varepsilon$. We call such fairness on ROCs of both the protected attributes as $\varepsilon_p$-Equalized ROC. Given a classifier not satisfying $\varepsilon_1$-Equalized ROC, we aim to design a post-processing method to transform the given (potentially unfair) classifier's output (scores) to a suitable randomized yet fair classifier. That is, the resultant classifier must satisfy $\varepsilon_1$-Equalized ROC. The resulting classifier is bound to get a reduction in the area under the curve (AUC) of its ROC. First, we introduce a threshold query model on the ROC curves for each protected group. With this query model, we provide a rigorous theoretical analysis of the minimal AUC loss to achieve $\varepsilon_1$-Equalized ROC. Next, we propose a linear time algorithm, namely FROC, to transform a given classifier's output to a classifier that satisfies $\varepsilon_1$-Equalized ROC. Under certain technical conditions, FROC achieves the theoretical optimal guarantees. We also study the performance of our FROC on multiple real-world datasets, with many trained classifiers.