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A family consisting of three people - P 1 , P 2 , and P 3 - belongs to a medical

ID: 3246837 • Letter: A

Question

A family consisting of three people - P1 , P2, and P3 - belongs to a medical clinic that always has a physician at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic exactly once and is randomly assigned to a station. One experimental outcome is (1, 2, 1), which means that P1 is assigned to station 1, P2 to station 2, and P3 to station 1.

(a) List the 27 possible outcomes. (Hint: First list the nine outcomes in which P1 goes to station 1, then the nine in which P1 goes to station 2, and finally the nine in which P1 goes to station 3; a tree diagram might help.)

{ (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }
{ (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 1), (1, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }
{ (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }
{ (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }
{ (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (2, 3, 1), (3, 3, 2), (3, 3, 3) }


(b) List all outcomes in the event A, that all three people go to the same station.

A = { (1, 1, 1), (2, 2, 2), (3, 3, 3) }A = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }    A = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (2, 1, 1), (2, 2, 2), (2, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }A = { (1, 1, 1), (2, 2, 2), (1, 3, 1) }A = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 1), (3, 3, 1), (3, 3, 2), (3, 3, 3) }



(c) List all outcomes in the event B, that all three people go to different stations.

B = { (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (2, 1, 3), (3, 2, 1) }B = { (1, 2, 3), (2, 3, 1), (1, 3, 2), (2, 1, 3), (3, 2, 1) }    B = { (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (3, 2, 1) }B = { (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (2, 1, 3), (3, 2, 2) }B = { (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 2, 3), (2, 1, 3), (3, 2, 1) }



(d) List all outcomes in the event C, that no one goes to station 1.

C = { (2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3), (3, 3, 2), (3, 2, 2), (3, 2, 3), (2, 3, 2) }C = { (1, 1, 1), (1, 1, 3), (1, 3, 3), (3, 3, 3), (3, 3, 1), (3, 1, 1), (3, 1, 3), (1, 3, 1) }     C = { (2, 2, 2), (2, 2, 1), (2, 1, 1), (1, 1, 1), (1, 1, 2), (1, 2, 2), (1, 2, 1), (2, 1, 2) }C = { (2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3), (3, 2, 2), (3, 2, 3), (2, 3, 2) }C = { (2, 2, 2), (2, 3, 3), (3, 3, 3), (3, 3, 2), (3, 2, 2), (3, 2, 3), (2, 3, 2) }


(e) Identify outcomes in the following events.
Bc:

Bc = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 3, 1), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 3), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }
Bc = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }
Bc = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }
Bc = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 3, 1), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 3) }
Bc = { (1, 1, 1), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 3, 1), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }


Cc:

Cc = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 1), (2, 3, 1), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 3, 1) }
Cc = { (1, 1, 2), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 2), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 2), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 2) }
Cc = { (1, 1, 3), (1, 2, 3), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 3), (2, 2, 3), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }
Cc = { (1, 1, 3), (1, 2, 3), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 3), (2, 2, 3),(2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }
Cc = { (1, 1, 2), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 2), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 1), (2, 3, 2), (3, 1, 2), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 2) }


A B:

A B = { (1, 1, 1), (2, 2, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (2, 1, 3), (3, 2, 1) }
A B = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (2, 1, 3), (3, 2, 1) }
A B = { (1, 1, 1), (2, 2, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (3, 2, 1) }
A B = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (2, 1, 1), (2, 2, 2), (2, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 2, 3), (2, 1, 3), (3, 2, 1) }
A B = the empty set


A B:

A B = the empty set
A B = { (1, 1, 1), (2, 2, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (2, 1, 3), (3, 2, 1) }
A B = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (2, 1, 3), (3, 2, 1) }
A B = { (1, 1, 1), (2, 2, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (3, 2, 1) }
A B = { (1, 1, 1), (1, 1, 2), (1, 1, 3), (2, 1, 1), (2, 2, 2), (2, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 2, 3), (2, 1, 3), (3, 2, 1) }


A C:

A C = { (2, 2, 2), (3, 3, 3) }A C = { (1, 1, 1), (3, 3, 3) }    A C = { (1, 1, 1), (2, 2, 2) }A C = { (2, 2, 2), (2, 2, 3), (3, 3, 2), (3, 3, 3) }A C = { (1, 1, 1), (1, 1, 3), (3, 3, 1), (3, 3, 3) }A C = { (1, 1, 1), (1, 1, 2), (2, 2, 1), (2, 2, 2) }

Explanation / Answer

a)the 27 possible outcomes:

{ (1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 3, 1), (1, 3, 2), (1, 3, 3), (2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 3, 1), (2, 3, 2), (2, 3, 3), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 3, 1), (3, 3, 2), (3, 3, 3) }

b)

all outcomes in the event A, that all three people go to the same station:

A = { (1, 1, 1), (2, 2, 2), (3, 3, 3) }

c)all outcomes in the event B, that all three people go to different stations:

B = { (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (2, 1, 3), (3, 2, 1)

d)all outcomes in the event C, that no one goes to station 1

C = { (2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3), (3, 3, 2), (3, 2, 2), (3, 2, 3), (2, 3, 2) }

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