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. Using the outcomes for the chance experiment, identify outcomes in each of the following events. Let A be the event that P₁ and P2 go to the same station, B be the event that all three people go to different stations, and C be the event that no one goes to station 2. (a) BC B = {(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)) B = {(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)) (b) 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)) lo c = {(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)) C= {(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)) c= {(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)) c= {(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)} (c) AUB AUB= {(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)) AUB= {(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)} AUB= {(1, 1, 1), (2, 2, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (3, 2, 1)) AUB= {(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)) AUB= the empty set (d) An B An B = the empty set An 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)} An 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)) An 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)) An 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 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. Using the outcomes for the chance experiment, identify outcomes in each of the following events. Let A be the event that P₁ and P2 go to the same station, B be the event that all three people go to different stations, and C be the event that no one goes to station 2. (a) BC B = {(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)) B = {(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)) (b) 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)) lo c = {(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)) C= {(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)) c= {(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)) c= {(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)} (c) AUB AUB= {(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)) AUB= {(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)} AUB= {(1, 1, 1), (2, 2, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (3, 2, 1)) AUB= {(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)) AUB= the empty set (d) An B An B = the empty set An 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)} An 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)) An 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)) An 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))
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please answer Part A, C and D
Transcribed Image Text: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.
Using the outcomes for the chance experiment, identify outcomes in each of the following events. Let A be the event that P₁ and P2 go to the same station, B be the event that all three people go to different stations, and C be the event that no one
goes to station 2.
(a) 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)}
(b) 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)}
сс
= {(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)}
(c) AUB
AUB= {(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)}
。 AUB= {(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)}
AUB = {(1, 1, 1), (2, 2, 2), (3, 3, 3), (1, 2, 3), (2, 3, 1), (3, 1, 2), (1, 3, 2), (3, 2, 1)}
AUB = {(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)}
AUB= the empty set
(d) An B
An B = the empty set
An 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)}
An 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)}
An 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))
An 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)}
Expert Solution
Step 1
Event(A) : P1 and P2 goes to same station
Event (B) : all three goes to different stations
Bc = all three doesn't go different stations (at least two go to same station)
Event (C) : no one goes to station 2
Cc = at least one goes to station 2
There will be (33 = 27) total outcomes
Total outcomes are
(P1,P2,P3) :
{(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)}
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