Distinguishing between a dangerous audio event like a gun firing and other non-life-threatening events, such as a plastic bag bursting, can mean the difference between life and death and, therefore, the necessary and unnecessary deployment of public safety personnel. Sounds generated by plastic bag explosions are often confused with real gunshot sounds, by either humans or computer algorithms. As a case study, the research reported in this paper offers insight into sounds of plastic bag explosions and gunshots. An experimental study in this research reveals that a deep learning-based classification model trained with a popular urban sound dataset containing gunshot sounds cannot distinguish plastic bag pop sounds from gunshot sounds. This study further shows that the same deep learning model, if trained with a dataset containing plastic pop sounds, can effectively detect the non-life-threatening sounds. For this purpose, first, a collection of plastic bag-popping sounds was recorded in different environments with varying parameters, such as plastic bag size and distance from the recording microphones. The audio clips’ duration ranged from 400 ms to 600 ms. This collection of data was then used, together with a gunshot sound dataset, to train a classification model based on a convolutional neural network (CNN) to differentiate life-threatening gunshot events from non-life-threatening plastic bag explosion events. A comparison between two feature extraction methods, the Mel-frequency cepstral coefficients (MFCC) and Mel-spectrograms, was also done. Experimental studies conducted in this research show that once the plastic bag pop sounds are injected into model training, the CNN classification model performs well in distinguishing actual gunshot sounds from plastic bag sounds.