Question

# Let A be the event that a given patient of a health clinic has the flu....

Let A be the event that a given patient of a health clinic has the flu. Let B be the event that a given patient of that same health clinic has a fever, and let C be the event that a given patient of that same health clinic has a cough. Assume that 5% of the patients of the clinic have the flu and that of those patients, 90% have a fever, 85% have a cough, and 97% have either a cough or a fever.

a.) Determine the probability that a patient at the health clinic with the flu has a fever and a cough.

b.) If 10.5% of the patients of the clinic who do not have the flue have a fever, are the events A and B independent?

c.) What is the probability that a given patient of the clinic with a fever has the flu if P(B l Ac) = .105?

d.) Let D be the event that a given patient of the same health clinic is male. If 3% of the health clinic's patients are males with the flu, and 60% of the clinic's patients are male, are the events A and D independent?

Please let me know if you need any further explanation. Thank you