Patients arriving at a hospital outpatient clinic can select one of three statio
ID: 3353193 • Letter: P
Question
Patients arriving at a hospital outpatient clinic can select one of three stations for service. Suppose that physicians are assigned randomly to the stations and that the patients thus have no station preference. The station selection of three patients arriving at the clinic at different times is observed. (a) Give the sample space for the experiment. (b) Let A be the event that each station receives a patient. List the sample points in A. (c) Let B be the event that all three patients go to the same station. List the sample points in B. (d) List the outcomes in AUB and An B. (e) Assuming outcomes in the sample space are equally likely, find P(B)Explanation / Answer
Part a)Three patients arriving at a hospital and randomly select stations.
Let A , B and C represent the event that patiants choose stations.
The sample space is then given by ,
S = {(AAA), (AAB), (AAC), (ABA), (ABB), (ABC), (ACA), (ACB), (ACC),
(BAA), (BAB), (BAC), (BBA), (BBB), (BBC), (BCA), (BCB), (BCC),
(CAA), (CAB), (CAC), (CBA), (CBB), (CBC), (CCA), (CCB), (CCC)}
Part b) Let A be the event that each station receives a patient then an outcome,
So A = {(ABC), (ACB), (BAC), (BCA), (CAB), (CBA)}
Part c) Let B be the event that all three patients go to the same station.
So B = {(AAA),(BBB),(CCC)}
Part d) AUB includes the all outcomes in A and B = { (ABC), (ACB), (BAC), (BCA), (CAB), (CBA),(AAA),(BBB),(CCC) }
AnB includes the common outcomes in A and B = null or 0
Part e)P(B) = number of outcomes in B / number of outcomes in S = 3/27 = 1/9
Thank you!!