We use a simple model to derive a mortality probability distribution for a patient as a function of days since diagnosis (considering diagnoses made between 25 February and 29 March 2020). The peak of the mortality probability is the 13th day after diagnosis. The overall shape and peak location of this probability curve are similar to the onset-to-death probability distribution in a case study using Chinese data. The total mortality probability of a COVID-19 patient in the US diagnosed between 25 February and 29 March is about 21%. We speculate that this high value is caused by severe under-testing of the population to identify all COVID-19 patients. With this probability, and an assumption that the true probability is 2.4%, we estimate that 89% of all SARS-CoV-2 infection cases were not diagnosed during this period. When the same method is applied to data extended to 25 April, we found that the total mortality probability of a patient diagnosed in the US after 1 April is about 6.4%, significantly lower than for the earlier period. We attribute this drop to increasingly available tests. Given the assumption that the true mortality probability is 2.4%, we estimate that 63% of all SARS-CoV-2 infection cases were not diagnosed during this period (1 - 25 April).