According to the data, a new AI based medical inexpensive diagnostic tool makes a correct diagnosis of a specific disease 85% of the time. In other words, it makes an incorrect diagnosis 15% of the time. A hospital in France wants to assess and prepare for potentially misdiagnosed patients:

1. Out of 50 patients that come in a particular week, what is the probability that at least 10 will be misdiagnosed?
2. Out of 50 patients that come in a particular week, what is the probability that between 5 and 15 (including 5 and 15) will be misdiagnosed?