DTSA 5001 - Probability Theory: Foundation for Data Science
Comprehensive Resource To Help You Ace 2026-2027 Exams
Includes Frequently Tested Questions With ELABORATED
100% Correct COMPLETE SOLUTIONS
Guaranteed Pass First Attempt!! Current Update!!
1. What does rnorm() do in R? - Correct Answer: Generates random
Normal variates with a specified mean and standard deviation.
2. What is factor() used for in R? - Correct Answer: Represents categorical
(qualitative) variables.
3. What does hist() do in R? - Correct Answer: Creates a histogram.
4. What is logical indexing? - Correct Answer: Indexing a data structure
based on specified logical conditions.
5. What does sample() do in R? - Correct Answer: Randomly selects a
sample from a vector.
6. What does colMeans() do in R? - Correct Answer: Calculates the mean
of each column in a matrix.
7. What does summary() do in R? - Correct Answer: Produces numerical
summaries of a dataset.
,8. What is a sample space? - Correct Answer: The set of all possible
outcomes.
9. What is an event in probability? - Correct Answer: A subset of the
sample space.
10.What is the cardinality of a set? - Correct Answer: The number of
elements in the set.
11.What does Axiom 1 of probability state? - Correct Answer: For any
event A, 0 ≤ P(A) ≤ 1.
12.What does Axiom 2 of probability state? - Correct Answer: P(S) = 1.
13.What does Axiom 3 of probability state? - Correct Answer: The
probability of mutually exclusive events occurring is the sum of their
individual probabilities.
14.What is the formula for P(A ∪ B)? - Correct Answer: P(A) + P(B) − P(A ∩
B).
15.What is a permutation? - Correct Answer: An arrangement of objects
where order is important.
16.What is a combination? - Correct Answer: A selection of objects where
order does not matter.
, 17.What is the formula for combinations? - Correct Answer: C(n, k) = n! /
[k!(n − k)!].
18.What is the formula for P(A ∪ B ∪ C)? - Correct Answer: P(A) + P(B) +
P(C) − P(A∩B) − P(B∩C) − P(A∩C) + P(A∩B∩C).
19.What is conditional probability? - Correct Answer: The probability of an
event occurring given that another event has already occurred.
20.What is the formula for P(A|B)? - Correct Answer: P(A ∩ B) / P(B).
21.What is Bayes' Theorem? - Correct Answer: P(A|B) = [P(B|A) × P(A)] /
P(B).
22.What is the Law of Total Probability (LTP)? - Correct Answer: The
probability of an event equals the sum of its probabilities across all possible
conditions.
23.What is B expressed under the Law of Total Probability? - Correct
Answer: (B ∩ A) ∪ (B ∩ Aᶜ).
24.What is the Law of Total Probability formula for P(B)? - Correct Answer:
P(B|A)P(A) + P(B|Aᶜ)P(Aᶜ).
25.What are independent events? - Correct Answer: Events where the
occurrence of one does not affect the probability of the other.
Comprehensive Resource To Help You Ace 2026-2027 Exams
Includes Frequently Tested Questions With ELABORATED
100% Correct COMPLETE SOLUTIONS
Guaranteed Pass First Attempt!! Current Update!!
1. What does rnorm() do in R? - Correct Answer: Generates random
Normal variates with a specified mean and standard deviation.
2. What is factor() used for in R? - Correct Answer: Represents categorical
(qualitative) variables.
3. What does hist() do in R? - Correct Answer: Creates a histogram.
4. What is logical indexing? - Correct Answer: Indexing a data structure
based on specified logical conditions.
5. What does sample() do in R? - Correct Answer: Randomly selects a
sample from a vector.
6. What does colMeans() do in R? - Correct Answer: Calculates the mean
of each column in a matrix.
7. What does summary() do in R? - Correct Answer: Produces numerical
summaries of a dataset.
,8. What is a sample space? - Correct Answer: The set of all possible
outcomes.
9. What is an event in probability? - Correct Answer: A subset of the
sample space.
10.What is the cardinality of a set? - Correct Answer: The number of
elements in the set.
11.What does Axiom 1 of probability state? - Correct Answer: For any
event A, 0 ≤ P(A) ≤ 1.
12.What does Axiom 2 of probability state? - Correct Answer: P(S) = 1.
13.What does Axiom 3 of probability state? - Correct Answer: The
probability of mutually exclusive events occurring is the sum of their
individual probabilities.
14.What is the formula for P(A ∪ B)? - Correct Answer: P(A) + P(B) − P(A ∩
B).
15.What is a permutation? - Correct Answer: An arrangement of objects
where order is important.
16.What is a combination? - Correct Answer: A selection of objects where
order does not matter.
, 17.What is the formula for combinations? - Correct Answer: C(n, k) = n! /
[k!(n − k)!].
18.What is the formula for P(A ∪ B ∪ C)? - Correct Answer: P(A) + P(B) +
P(C) − P(A∩B) − P(B∩C) − P(A∩C) + P(A∩B∩C).
19.What is conditional probability? - Correct Answer: The probability of an
event occurring given that another event has already occurred.
20.What is the formula for P(A|B)? - Correct Answer: P(A ∩ B) / P(B).
21.What is Bayes' Theorem? - Correct Answer: P(A|B) = [P(B|A) × P(A)] /
P(B).
22.What is the Law of Total Probability (LTP)? - Correct Answer: The
probability of an event equals the sum of its probabilities across all possible
conditions.
23.What is B expressed under the Law of Total Probability? - Correct
Answer: (B ∩ A) ∪ (B ∩ Aᶜ).
24.What is the Law of Total Probability formula for P(B)? - Correct Answer:
P(B|A)P(A) + P(B|Aᶜ)P(Aᶜ).
25.What are independent events? - Correct Answer: Events where the
occurrence of one does not affect the probability of the other.
