A patient comes into a doctor’s office with a high fever, co…

A patient comes into a doctor’s office with a high fever, coughing, and loss of smell.  He believes the patient has COVID and starts treating them immediately.  Is the doctor’s diagnosis of COVID an classical, subjective, or empirical probability?  Explain your reasoning.

An old farm is analyzing water samples from 76 water pipes f…

An old farm is analyzing water samples from 76 water pipes for pollution. Five of the pipes contain dangerously high levels of lead. Six of the pipes are randomly selected from the sample.  How many ways can one polluted pipe and five non-polluted pipes be chosen?  What is the probability of choosing one polluted pipe and five non-polluted pipes?