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In recent years, deep learning-based technologies have become widely used in the medical area with remarkable success. The output of many of these methods, however, has excessive confidence levels and the majority of them cannot provide numerical guarantees. There is no way they could be effective, and they might even cause permanent harm. Therefore, the approximation of Bayesian and Ensemble learning techniques are considered as uncertainty quantification approaches to take on such a problem. In this study, we implement and assess three UQ models for categorising breast tumour tissues. A few examples of these techniques include the Bayesian Ensemble, the MCD Ensemble, and the Mont Carlo Dropout (MCD) approach. In addition, the present study takes into account a transfer learning technique and a pre-trained CNN in order to boost the classification's accuracy and remove the negative effects of the study's small data collection in Wisconsin Diagnostic Breast Cancer (WDBC). Novel performance criteria are used to assess estimated uncertainty, and the three proposed models are compared based on their capacity to quantify the reliability of classification. In the study, we conducted quantitative and qualitative analyses to indicate that models exhibit substantial ambiguity in misclassifications, which is critical for establishing the frequency of medical diagnosis hazards. Therefore, we hope to determine whether the deep neural