Homework 1
Seoul National University, Spring 2026
Due 23:59 Thursday, 3/19/2026
No late submission is accepted.
Note: The textbook for this course is 10th, Global Edition (2019),
not the 10th Edition (2022). Please check carefully. If you use
the wrong edition, any answers based on it will receive no
points.
1. Textbook problems
• Chapter 1 Problems 19, 35
• Chapter 1 Theoretical Exercises 9, 21
• Chapter 2 Problems 40, 43, 52
• Chapter 2 Theoretical Exercises 16, 19
2. Prove that
(a) For any sequence of events E1 , E2 . . . . with Ei ∩ Ej = ∅ for all i ̸= j,
!
∞
∞
[
X
P
Ei =
P (Ei )
i=1
i=1
implies
P
n
[
!
Ei
i=1
=
n
X
P (Ei )
i=1
for any finite sequence of events E1 , E2 , . . . , En with Ei ∩ Ej = ∅
for all i ̸= j.
(b) For any finite sequence of events E1 , E2 , . . . , En ,
!
n
n
[
X
P
Ei ≤
P (Ei ).
i=1
i=1
1