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 all three people 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 3. (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)} 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)} (c) 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 (d) A ∩ B A ∩ B = the empty setA ∩ 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)} (e) 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)}
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 all three people 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 3. (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)} 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)} (c) 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 (d) A ∩ B A ∩ B = the empty setA ∩ 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)} (e) 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)}
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
Related questions
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.
Using the outcomes for the chance experiment, identify outcomes in each of the following events. Let A be the event that all three people 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 3.
(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)} 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)}
(c)
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
(d)
A ∩ B
A ∩ B = the empty setA ∩ 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)}
(e)
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)}
Expert Solution
Step 1
Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a time so we are answering the first three as you have not mentioned which of these you are looking for. Please re-submit the question separately for the remaining sub-parts.
It is given that:
A be the event that all the three people go to the same station.
B be the event that all the three people go to different stations.
and, C be the event that no one goes to the station 3.
and denotes that the person 1 is assigned to the station 1 , person 2 to the station 2 and person 3 to the station 1.
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