Question: A sample of 400 patients from a group medical plan received treatment
ID: 2946935 • Letter: Q
Question
Question: A sample of 400 patients from a group medical plan received treatment from either a physician or a nurse practitioner. Their medical care was then rated as satisfactory or unsatisfactory. Answer the questions based on the results summarized in the table below:
Physician
Total
Satisfactory
A. Are the events Physician and Nurse-Practitioner mutually exclusive? Explain why or why not.
B. What is the probability that a patient received treatment that was Satisfactory and from a Physician?
C. What is the probability that a patient received treatment that was from a Physician or was Satisfactory?
D. What is the probability that a patient received Satisfactory treatment, given that the patient was treated by a Nurse Practitioner?
E. Are the events Physician and Satisfactory independent events? Compare probabilities to decide, and explain your reasoning using one of these phrases: equally likely, more likely, less likely.
Physician
Nurse PractitionerTotal
Satisfactory
90 161 251 Unsatisfactory 37 112 149 Total 127 273 400Explanation / Answer
a) There is no one in the table who is both a physicial, and a nurse practitioner, therefore Yes the 2 events are mutually exclusive.
b) The probability that the treatment was satisfactory and from physician is computed here as:
= 90 / 400
= 0.225
Therefore 0.225 is the required probability here.
c) Probability that it is from a physicial or satisfactory is computed here as:
= (251 + 127 - 90 ) / 400
= 288 / 400
= 0.72
Therefore 0.72 is the required probability here.
d) Given that the patient was treated by a nurse practitioner, probability that it was satisfactory is computed as:
= 161 / 273
= 0.5897
Therefore 0.5897 is the required probability here.
e) P( physician ) = 127 / 400 = 0.3175
P( satisfactory ) = 251 / 400 = 0.6275
P( satisfactory and physician ) = 90 / 400 = 0.225
P( physician ) P( satisfactory ) = 0.3175*0.6275 = 0.1992 which is not equal to 0.225
Therefore the 2 events are not independent .
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