events and find P(A), P(B), and P(C) Patients arriving at a hospital outpatient

Question

events and find P(A), P(B), and P(C) 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 therefore have no station preference. Three patients arrive at the clinic and their selection of stations is observed. 2.34 List the sample points for the experiment. Let A be the event that each station receives a patient. List the sample points in A. Make a reasonable assignment of probabilities to the sample points and find P(A). a c

Explanation / Answer

Let S1 shows the event that patient selects station1, S2 shows the event that patient selects station2 and S3 shows the event that patient selects station 3.

(a)

Each of the three patients can select station in three ways so possible outcomes in the sample space is 3*3 *3 = 27

Following table shows all the outcomes:

(b)

Following table list the outcomes in event A:

(c)

Since each of the 27 outcomes are equally likley so each outcome of sample space has probability 1 / 27.

Event A has 6 outcomes, so probability of event A is

P(A) = 6 / 27 = 2 / 9

Outcomes Patient 1 Patient 2 Pateint 3 S1 S1 S1 S1 S1 S2 S1 S1 S3 S1 S2 S1 S1 S2 S2 S1 S2 S3 S1 S3 S1 S1 S3 S2 S1 S3 S3 S2 S1 S1 S2 S1 S2 S2 S1 S3 S2 S2 S1 S2 S2 S2 S2 S2 S3 S2 S3 S1 S2 S3 S2 S2 S3 S3 S3 S1 S1 S3 S1 S2 S3 S1 S3 S3 S2 S1 S3 S2 S2 S3 S2 S3 S3 S3 S1 S3 S3 S2 S3 S3 S3

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