The Sickwell Rehabilitation facility receives 30%, 25%, and 45% of its patients from Aorta Hospital, Bursitis Hospital, and, Clavicle Hospital, respectively. It is known that Staphylococcus infection occurs in 20% of patients from Aorta Hospital, in 5% of patients from Bursitis Hospital, and in 10% of patients from Clavicle Hospital.

a.What is the probability of randomly selecting a patient that is both from Clavicle Hospital and has Staphylococcusinfection?

b.Find the probability that a randomly selected patient has Staphylococcus infection.

c.If it is known that a patient came from Bursitis Hospital, what is the probability that they have Staphylococcusinfection?

d.If it is known that a patient has Staphylococcus infection, what is the probability that they came from Aorta Hospital?

e.If it is known that a patient has Staphylococcus infection, what is the probability that they came from Bursitis Hospital?

f.If it is known that a patient has Staphylococcus infection, what is the probability that they came from Clavicle Hospital?