Accredited Test Bank Solution For First
Course in Probability 10th Edition by
Sheldon Ross
[All Lessons Included]
Complete Chapter Solution Manual
are Included (Ch.1 to Ch.8)
• Rapid Download
• Quick Turnaround
• Complete Chapters Provided
, Table of Contents are Given Below
1. Combinatorial Analysis
• 1.1 Introduction
• 1.2 The Basic Principle of Counting
• 1.3 Permutations
• 1.4 Combinations
• 1.5 Multinomial Coefficients
• 1.6 Integer-Solution Counts
• Summary, Problems, Exercises, Self-Tests
2. Axioms of Probability
• 2.1 Introduction
• 2.2 Sample Space & Events
• 2.3 Probability Axioms
• 2.4 Basic Propositions
• 2.5 Equally Likely Outcomes
• 2.6 Probability as a Set Function
• 2.7 Belief Interpretation
• Summary, Problems, Exercises, Self-Tests
3. Conditional Probability and Inference
• Conditional Probabilities, Bayes’s Formula, Independence, etc.
4. Random Variables
• Discrete RVs, expectation, variance, Bernoulli/Binomial, Poisson, CDF properties, sums
5. Continuous Random Variables
6. Jointly Distributed Random Variables
• Joint/marginal distributions, independence, conditional distributions, order statistics, sums/functions of
RVs
7. Properties of Expectation
• Linearity, covariance, conditional expectation, moment-generating functions, multivariate normal
8. Limit Theorems
• Strong Law of Large Numbers, Central Limit Theorem, probability inequalities (Markov, Chebyshev,
Chernoff bounds)
PAGE 1
,Question 1. In a set of 5 distinct books, how many ways can they be arranged on a
shelf?
A) 120
B) 60
C) 25
D) 720
Answer: A
Explanation: The number of arrangements of 5 distinct objects is 5! = 120, which is
permutations of 5 objects.
Question 2. How many different 3-element subsets can be formed from a set of 10
elements?
A) 120
B) 210
C) 720
D) 45
Answer: B
Explanation: The number of combinations of 10 elements taken 3 at a time is
C(10,3) = 10! / (3! * 7!) = 120.
Question 3. How many permutations are there of the letters in the word
"PROBABILITY" considering repeated letters?
PAGE 2
, A) 11! / (2! * 2! * 2!)
B) 13! / (2! * 3! * 2!)
C) 11! / (2! * 2! * 2! * 2!)
D) 13! / (2! * 2! * 2! * 2! * 2!)
Answer: B
Explanation: The word "PROBABILITY" has 11 letters with repetitions: B (2), I
(2), and the rest unique. Total arrangements: 11! / (2! * 2! * 2!) = =
4989600.
Question 4. How many solutions are there to the equation x + y + z = 7 with x, y, z
≥ 0?
A) 21
B) 35
C) 28
D) 15
Answer: C
Explanation: Number of non-negative integer solutions is C(7+3-1, 3-1) = C(9,2) =
36, but since the sum is 7, the correct count is 28 solutions.
Question 5. Using the basic principle of counting, how many 4-digit numbers have
all digits distinct?
A) 9000
B) 5040
PAGE 3
Course in Probability 10th Edition by
Sheldon Ross
[All Lessons Included]
Complete Chapter Solution Manual
are Included (Ch.1 to Ch.8)
• Rapid Download
• Quick Turnaround
• Complete Chapters Provided
, Table of Contents are Given Below
1. Combinatorial Analysis
• 1.1 Introduction
• 1.2 The Basic Principle of Counting
• 1.3 Permutations
• 1.4 Combinations
• 1.5 Multinomial Coefficients
• 1.6 Integer-Solution Counts
• Summary, Problems, Exercises, Self-Tests
2. Axioms of Probability
• 2.1 Introduction
• 2.2 Sample Space & Events
• 2.3 Probability Axioms
• 2.4 Basic Propositions
• 2.5 Equally Likely Outcomes
• 2.6 Probability as a Set Function
• 2.7 Belief Interpretation
• Summary, Problems, Exercises, Self-Tests
3. Conditional Probability and Inference
• Conditional Probabilities, Bayes’s Formula, Independence, etc.
4. Random Variables
• Discrete RVs, expectation, variance, Bernoulli/Binomial, Poisson, CDF properties, sums
5. Continuous Random Variables
6. Jointly Distributed Random Variables
• Joint/marginal distributions, independence, conditional distributions, order statistics, sums/functions of
RVs
7. Properties of Expectation
• Linearity, covariance, conditional expectation, moment-generating functions, multivariate normal
8. Limit Theorems
• Strong Law of Large Numbers, Central Limit Theorem, probability inequalities (Markov, Chebyshev,
Chernoff bounds)
PAGE 1
,Question 1. In a set of 5 distinct books, how many ways can they be arranged on a
shelf?
A) 120
B) 60
C) 25
D) 720
Answer: A
Explanation: The number of arrangements of 5 distinct objects is 5! = 120, which is
permutations of 5 objects.
Question 2. How many different 3-element subsets can be formed from a set of 10
elements?
A) 120
B) 210
C) 720
D) 45
Answer: B
Explanation: The number of combinations of 10 elements taken 3 at a time is
C(10,3) = 10! / (3! * 7!) = 120.
Question 3. How many permutations are there of the letters in the word
"PROBABILITY" considering repeated letters?
PAGE 2
, A) 11! / (2! * 2! * 2!)
B) 13! / (2! * 3! * 2!)
C) 11! / (2! * 2! * 2! * 2!)
D) 13! / (2! * 2! * 2! * 2! * 2!)
Answer: B
Explanation: The word "PROBABILITY" has 11 letters with repetitions: B (2), I
(2), and the rest unique. Total arrangements: 11! / (2! * 2! * 2!) = =
4989600.
Question 4. How many solutions are there to the equation x + y + z = 7 with x, y, z
≥ 0?
A) 21
B) 35
C) 28
D) 15
Answer: C
Explanation: Number of non-negative integer solutions is C(7+3-1, 3-1) = C(9,2) =
36, but since the sum is 7, the correct count is 28 solutions.
Question 5. Using the basic principle of counting, how many 4-digit numbers have
all digits distinct?
A) 9000
B) 5040
PAGE 3
