Homework 2 Introduction to Probability Solutions
(80 points)
1. (10 points, 5 points each)
a. A reasonable sample space consists of the number of papers that are sold by the
newspaper boy, S1 = {0, 1, 2, …, 9, 10}. Another one can be the number of
papers that are demanded, S2 = {0, 1, 2, …, 10,11, …}.
For S1, the event sets are as follows:
A = {5, 6, 7, …, 10}, B = {0, 1, 2, 3, 4, 5}, C = {5}.
For S2, the event sets are:
A = {5, 6, 7, …}, B = {0, 1, 2, 3, 4, 5}, C = {5}.
b. A reasonable sample space consists of pairs which includes the number of
papers that are sold in each day, S = S1 × S1 = {(0,0), (0,1), (0,2),…,(0,10), (1,0),
(1,1), (1,2),…,(1,10), …, (10,0),(10,1),(10,2),…,(10,10)}. For sample space S,
event sets are as follows:
A = {(5,0), (5,1), …, (5,10), (6,0), (6,1), (6,2), …,(6,10), …,(10,0), (10,1), (10, 2),
…, (10,10)}
B = {(0,5), (0,6), …, (0,10), (1,5), (1,6), …, (1,10), …, (10,5), (10,6), …,(10,10)}
C = {(5,5), (5,6), …,(5,10), (6,5), (6,6), …, (6,10), …, (10,5), (10,6), …,(10,10)}
2.
(16 points, 4 points each)
The probabilities of different events are given in figure above. Using the diagram,
we have
a)
P(A)
= 0.8
b)
P(B)
= 0.5
c)
)
(
B
A
P
∪
= 0.9
d)
)
(
B
A
P
∪
= 0.6
A
B
0.4
0.1
0.1
0.4