1
Homework 2 (13 points)
due Jan 27
(1.3 pts.) 2.4 (6-sided die)de. Suppose that one die is rolled and that you observe the
number of dots facing up.
From the last problem set:
The sample space includes all of the possible outcomes or
= {1, 2, 3, 4, 5, 6}
A = {2, 4, 6}
B = {4, 5, 6}
C = {1, 2}
D = {3}
d) Determine which of the following collections of events are mutually exclusive and
explain your answers: A and B, B and C, A, C, and D.
A and B are not mutually exclusive because 4 and 6 are in both of them
B and C are mutually exclusive because there are no elements in common.
A, C and D: A and C are not mutually exclusive because 2 is in both of them, therefore A, C and
D are not mutually exclusive. Note that A and D are mutually exclusive and C and D are
mutually exclusive.
e) Are there three mutually exclusive events amount A, B, C, and D? four?
A is only mutually exclusive with D
B is mutually exclusive with C and is mutually exclusive with D.
As mentioned in part (d), C and D are mutually exclusive.
Therefore, B, C, and D are mutually exclusive but A, B, C, and D are not.
(1.5 pts.) #1. Let A, B, and C be events of a sample space. Write a mathematical
expression for each of the following events. Hint: Problem 2.13
a) C occurs but B doesn't occur.
C ∩ B
c
b) Exactly two of A, B and C occur.
(A ∩ B ∩ C
c
) U (A ∩ B
c
∩ C) U (A
c
∩ B ∩ C)
The two can be either A and B, A and C or B and C
c) At most one of A, B, and C occur.
(A
c
∩ B
c
∩ C
c
) U (A ∩ B
c
∩ C
c
) U (A
c
∩ B ∩ C
c
) U (A
c
∩ B
c
∩ C)
At most one means, none occur, or A occurs or B occurs or C occurs.