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Cancer is a disease caused by uncontrollable cell growth. The disease is a constant subject of concern due to unavailability of treatment at a severe level. Patients who have suffered from the disease have the chance of getting saved if this fatal illness is identified in the beginning stage. The survival chance will be very low if it is detected in the final stage of cancer. As the patients could not survive in their last stage, to cure their disease, an early diagnosis is a key issue and is vital. For the classification of cancer, Gaussian Naïve Bayes is implemented in this work. By exerting it on two datasets, the algorithm is tested, in which the Wisconsin Breast Cancer Dataset (WBCD) is considered as earliest one and the next one is the Lung Cancer Dataset. The assessment result of the suggested algorithm attained 90% accuracy in the prediction of lung cancer, and in predicting breast cancer, the accuracy is 98%.