Malaria is a debilitating and potentially deadly parasitic infection that is mostly preventable and curable, yet many developing countries lack the necessary resources. The West African country of Guinea has the highest rate of malaria in the world, with 75% of its population infected. A physician from Doctors Without Borders sees 6 patients in a given hour. Assume that patient visits are independent.
(a) What is the distribution of the count of patients who are infected with malaria among the 6 patients the doctor sees? Explain your reasoning.
(b) What is the probability that at most five patients are infected?