Question

Let A be the event that a given patient of a health clinic has coronavirus. Let B be the event that a given patient of that some 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 coronavirus and that of those patients, 90% have a fever, 85% have a cough and 97% have either a cough or a fever.

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

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

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

Answer 1

The following probabilities are given.

Also, 10.5% of the patients of the clinic who do not have corona virus have a fever.

i.e., .

Now,

and,

Now . So the events A and B are not independent.

The probability that a given patient of the clinic with a fever has the corona virus

It is given that .

Since , the events A and D are independent.