At the end of 2019, the World Health Organization (WHO) referred that the Public Health Commission of Hubei Province, China, re- ported cases of severe and unknown pneumonia, characterized by fever, malaise, dry cough, dyspnoea and respiratory failure, which occurred in the urban area of Wuhan. A new coronavirus, SARS- CoV-2, was identified as responsible for the lung infection, now called COVID-19 (coronavirus disease 2019). Since then there has been an exponential growth of infections and at the beginning of March 2020 the WHO declared the epidemic a global emergency. An early diagnosis of those carrying the virus becomes crucial to contain the spread, morbidity and mortality of the pandemic. The definitive diagnosis is made through specific tests, among which imaging tests play an important role in the care path of the pa- tient with suspected or confirmed COVID-19. Patients with serious COVID-19 typically experience viral pneumonia. In this paper we launch the idea to use the Multiple Instance Learning paradigm to classify pneumonia X-ray images, consider- ing three different classes: radiographies of healthy people, radio- graphies of people with bacterial pneumonia and of people with viral pneumonia. The proposed algorithms, which are very fast in practice, appear promising especially if we take into account that no preprocessing technique has been used.