DTSA 5001 - Probability Theory:
Foundation for Data Science Questions
and Answers Graded A+
What is the probability of an event?
✔✔A measure of the likelihood that the event will occur.
What is the sample space in probability theory?
✔✔The set of all possible outcomes of a random experiment.
What does the complement of an event represent?
✔✔The event that the original event does not occur.
How is the probability of the union of two independent events calculated?
✔✔By adding the probabilities of each event and subtracting the probability of both events
occurring together.
What does a random variable represent in probability theory?
✔✔A numerical outcome of a random experiment.
1
,What is the difference between discrete and continuous random variables?
✔✔Discrete random variables take specific values, while continuous random variables can take
any value within a range.
What is the expected value of a random variable?
✔✔The weighted average of all possible values that the random variable can take, weighted by
their probabilities.
What is the variance of a random variable?
✔✔A measure of how much the values of a random variable differ from the expected value.
What does the standard deviation of a random variable represent?
✔✔The square root of the variance, showing how spread out the values of the random variable
are.
What is a probability distribution?
✔✔A function that describes the likelihood of different outcomes for a random variable.
2
,What is the difference between a binomial distribution and a normal distribution?
✔✔A binomial distribution models the number of successes in a fixed number of trials, while a
normal distribution is continuous and symmetric.
What is the law of total probability?
✔✔A rule for finding the probability of an event by considering all possible ways the event can
occur, through a partition of the sample space.
What is Bayes’ Theorem used for in probability theory?
✔✔It calculates the probability of an event based on prior knowledge of related events.
What is the conditional probability of an event?
✔✔The probability of an event occurring given that another event has already occurred.
What is a random process in probability theory?
✔✔A collection of random variables indexed by time or space.
3
, What does the Central Limit Theorem state?
✔✔The distribution of the sum (or average) of a large number of independent, identically
distributed random variables approaches a normal distribution, regardless of the original
distribution.
What is the difference between independent and dependent events?
✔✔Independent events have no effect on each other’s occurrence, while dependent events
influence each other.
What is the probability of a dependent event?
✔✔It is the product of the probability of the first event and the conditional probability of the
second event given the first.
What is the concept of "mutually exclusive events" in probability?
✔✔Two events are mutually exclusive if they cannot occur at the same time.
What is the law of large numbers in probability theory?
✔✔It states that as the number of trials increases, the sample mean will get closer to the expected
value.
4
Foundation for Data Science Questions
and Answers Graded A+
What is the probability of an event?
✔✔A measure of the likelihood that the event will occur.
What is the sample space in probability theory?
✔✔The set of all possible outcomes of a random experiment.
What does the complement of an event represent?
✔✔The event that the original event does not occur.
How is the probability of the union of two independent events calculated?
✔✔By adding the probabilities of each event and subtracting the probability of both events
occurring together.
What does a random variable represent in probability theory?
✔✔A numerical outcome of a random experiment.
1
,What is the difference between discrete and continuous random variables?
✔✔Discrete random variables take specific values, while continuous random variables can take
any value within a range.
What is the expected value of a random variable?
✔✔The weighted average of all possible values that the random variable can take, weighted by
their probabilities.
What is the variance of a random variable?
✔✔A measure of how much the values of a random variable differ from the expected value.
What does the standard deviation of a random variable represent?
✔✔The square root of the variance, showing how spread out the values of the random variable
are.
What is a probability distribution?
✔✔A function that describes the likelihood of different outcomes for a random variable.
2
,What is the difference between a binomial distribution and a normal distribution?
✔✔A binomial distribution models the number of successes in a fixed number of trials, while a
normal distribution is continuous and symmetric.
What is the law of total probability?
✔✔A rule for finding the probability of an event by considering all possible ways the event can
occur, through a partition of the sample space.
What is Bayes’ Theorem used for in probability theory?
✔✔It calculates the probability of an event based on prior knowledge of related events.
What is the conditional probability of an event?
✔✔The probability of an event occurring given that another event has already occurred.
What is a random process in probability theory?
✔✔A collection of random variables indexed by time or space.
3
, What does the Central Limit Theorem state?
✔✔The distribution of the sum (or average) of a large number of independent, identically
distributed random variables approaches a normal distribution, regardless of the original
distribution.
What is the difference between independent and dependent events?
✔✔Independent events have no effect on each other’s occurrence, while dependent events
influence each other.
What is the probability of a dependent event?
✔✔It is the product of the probability of the first event and the conditional probability of the
second event given the first.
What is the concept of "mutually exclusive events" in probability?
✔✔Two events are mutually exclusive if they cannot occur at the same time.
What is the law of large numbers in probability theory?
✔✔It states that as the number of trials increases, the sample mean will get closer to the expected
value.
4
