Answer:
a) ![\Omega=\{1, 2, 31, 32, 41, 42, 341, 342, 431, 432\}](https://tex.z-dn.net/?f=%5COmega%3D%5C%7B1%2C%202%2C%2031%2C%2032%2C%2041%2C%2042%2C%20341%2C%20342%2C%20431%2C%20432%5C%7D)
b) A={1, 2}
c) B={341, 342, 431, 432}
d) C={31, 32, 341, 342, 431, 432}
e) D={1, 31, 41, 341, 431}
f) E={41, 42, 341, 342, 431, 432}
Step-by-step explanation:
We know that four candidates are to be interviewed for a job. Two of them, numbered 1 and 2, are qualified, and the other two, numbered 3 and 4, are not.
a) We get a set of all possible outcomes:
![\Omega=\{1, 2, 31, 32, 41, 42, 341, 342, 431, 432\}](https://tex.z-dn.net/?f=%5COmega%3D%5C%7B1%2C%202%2C%2031%2C%2032%2C%2041%2C%2042%2C%20341%2C%20342%2C%20431%2C%20432%5C%7D)
b) Let A be the event that only one candidate is interviewed.
We get a set of all possible outcomes:
A={1, 2}
c) Let B be the event that three candidates are interviewed.
We get a set of all possible outcomes:
B={341, 342, 431, 432}
d) Let C be the event that candidate 3 is interviewed.
We get a set of all possible outcomes:
C={31, 32, 341, 342, 431, 432}
e) Let D be the event that candidate 2 is not interviewed.
We get a set of all possible outcomes:
D={1, 31, 41, 341, 431}
f) Let E be the event that candidate 4 is interviewed.
We get a set of all possible outcomes:
E={41, 42, 341, 342, 431, 432}
We conclude that the events A and E are mutually exclusive.
We conclude that the events B and E are not mutually exclusive.
We conclude that the events C and E are not mutually exclusive.
We conclude that the events D and E are not mutually exclusive.