1-4.8 A traffic survey on a busy highway reveals that one of every four vehicles is a truck. This survey also established that one-eighth of all automobiles are unsafe to drive and one-twentieth of all trucks are unsafe to drive. 42 CHAPTER 1 INTRODUCTION a) What is the probability that the next vehicle to pass a given point is an unsafe truck? b) What is the probability that the next vehicle will be a truck, given that it is unsafe? c) What is the probability that the next vehicle that passes a given point will be a truck, given that the previous vehicle was an automobile? 1-5.1 Prove that a space $ containing n elements has 2" subsets. Hint: Use the binomial expansion for (1 + x)". 1-5.2 A space S is defined as S (1, 3, 5, 7, 9, 11) and three subsets as A=(1, 3, 5), B (7, 9, 11), C = {1, 3, 9, 11) Find: AUB ANBOC (BNC) BUC Α A-C AUC B C-A АОВ T A-B Anc A B (A-B)UB BOC A B (A-B) UC 1-5.3 Draw and label the Venn diagram for Problem 1-4.4. 1-5.4 Using the algebra of sets show that the following relations are true. a) AU (ANB) = A b) AU (BNC) (AUB) N (AUC) c) AU (ANB)=AUB d) (ANB) U (ANB) U (ANB) = A
1-4.8 A traffic survey on a busy highway reveals that one of every four vehicles is a truck. This survey also established that one-eighth of all automobiles are unsafe to drive and one-twentieth of all trucks are unsafe to drive. 42 CHAPTER 1 INTRODUCTION a) What is the probability that the next vehicle to pass a given point is an unsafe truck? b) What is the probability that the next vehicle will be a truck, given that it is unsafe? c) What is the probability that the next vehicle that passes a given point will be a truck, given that the previous vehicle was an automobile? 1-5.1 Prove that a space $ containing n elements has 2" subsets. Hint: Use the binomial expansion for (1 + x)". 1-5.2 A space S is defined as S (1, 3, 5, 7, 9, 11) and three subsets as A=(1, 3, 5), B (7, 9, 11), C = {1, 3, 9, 11) Find: AUB ANBOC (BNC) BUC Α A-C AUC B C-A АОВ T A-B Anc A B (A-B)UB BOC A B (A-B) UC 1-5.3 Draw and label the Venn diagram for Problem 1-4.4. 1-5.4 Using the algebra of sets show that the following relations are true. a) AU (ANB) = A b) AU (BNC) (AUB) N (AUC) c) AU (ANB)=AUB d) (ANB) U (ANB) U (ANB) = A
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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Transcribed Image Text:1-4.8 A traffic survey on a busy highway reveals that one of every four vehicles is a truck.
This survey also established that one-eighth of all automobiles are unsafe to drive and
one-twentieth of all trucks are unsafe to drive.
42
CHAPTER 1 INTRODUCTION
a) What is the probability that the next vehicle to pass a given point is an unsafe truck?
b) What is the probability that the next vehicle will be a truck, given that it is unsafe?
c) What is the probability that the next vehicle that passes a given point will be a truck,
given that the previous vehicle was an automobile?
1-5.1 Prove that a space $ containing n elements has 2" subsets. Hint: Use the binomial
expansion for (1 + x)".
1-5.2 A space S is defined as
S (1, 3, 5, 7, 9, 11)
and three subsets as
A=(1, 3, 5), B (7, 9, 11), C = {1, 3, 9, 11)
Find:
AUB
ANBOC
(BNC)
BUC
Α
A-C
AUC
B
C-A
АОВ
T
A-B
Anc
A B
(A-B)UB
BOC
A B
(A-B) UC
1-5.3 Draw and label the Venn diagram for Problem 1-4.4.
1-5.4 Using the algebra of sets show that the following relations are true.
a) AU (ANB) = A
b) AU (BNC) (AUB) N (AUC)
c) AU (ANB)=AUB
d) (ANB) U (ANB) U (ANB) = A
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