In a hospital 60% of the employees are certified medical professionals and 80% o

Question

In a hospital 60% of the employees are certified medical professionals and 80% of the employees are full-time. Ninety percent of the professionals are full-time.
a) what is the probability that the selected employee is a professional full-time employee?
b) what is the probability that the selected employee is a medical professional or a full-time employee?
c) Are being a medical professional employee and being a fulltimr employee two independent events?
d) What percentage of the full-timr employees of this hospital is skilled?

Explanation / Answer

P(professional)=0.6

P(full time)=0.8

P(full time|professional)=0.9

a)P(professional & full time)=0.6*0.9=0.54

b)P(professional or full time)=0.6+0.8-0.54=0.86

c)P(professional)*P(full time)=0.6*0.8=0.48 which is not equal to P(professional & full time)=0.54

Hence they are not independent

d)P(professional|full time)=0.54*0.8 =0.432

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