Patient clinic Probability Questions

[FaradayLaws]

Hello I have been stuck on these two probability questions.

Homework Statement

1) 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.
a List the sample points for the experiment.
b Let A be the event that each station receives a patient. List the sample points in A.
c Make a reasonable assignment of probabilities to the sample points and find P(A).


Attempt:
a) I think I may not be able to interpret the question properly. I'm understanding that the experiment is observing how three patients can be positioned in three stations for services. I'm not sure but the cardinality of the sample space is 3*2*1=6 ?and the points must satisfy
S1= Station 1, S2= Station 2, S3= Station 3
a= room a, b= room b, c= room c
The sample points must satisfy { (i,j) where i and j are combinations with regards to order of Station (S1,S2,S3) and Room ( a,b,c)}
I'm not sure this is the correct response.

b) Given that I've interpreted the question correctly, Sample Space of A= { (S1,a), (S1, b), (S1,c), (S2,a), (S2, b), (S2,c), (S3,a), (S3, b), (S3,c)}

c) Using the equiprobability assumption; each sample pt takes weight 1/6.

2) An accident victim will die unless in the next 10 minutes he receives some type A, Rh-positive
blood, which can be supplied by a single donor. The hospital requires 2 minutes to type a
prospective donor’s blood and 2 minutes to complete the transfer of blood. Many untyped
donors are available, and 40% of them have type A, Rh-positive blood. What is the probability
that the accident victim will be saved if only one blood-typing kit is available? Assume that
the typing kit is reusable but can process only one donor at a time.

Attempt:
I'm not sure how to solve this at all. I'm understanding that what's given to me is
P( type A)= 0.40
P( will be saved | only one blood type kit is avaible)= ?
Not sure how to process from here.



Thank you in advance.

 

[jbunniii]

Regarding the first problem, I think the intent is to assume that each patient chooses a station at random, and that the choice of one patient is independent of the choice of another.

I don't understand the distinction you are making between stations and "rooms." The latter aren't even mentioned in the problem statement.

The problem deals with two types of objects: patients and stations. You could therefore define the set of sample points (outcomes) as ordered triplets (i, j, k) with the meaning that patient 1 selects station i, patient 2 selects station j, and patient 3 selects station k.

Now answer this: how many different (i, j, k) samples are there, and what probability should be assigned for each one?

 

[FaradayLaws]

Thanks !

So the sample space contains 3^3= 27 possibilities and each sample point is associated with probability of 1/27.