1. What is probability?
Probability is a measure or estimation of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. What is the sample space?
The sample space is the set of all possible outcomes of a random experiment. It is denoted by the symbol S.

3. What is an event?
An event is a subset of the sample space, representing a specific outcome or set of outcomes of a random experiment.

4. What is the difference between independent and dependent events?
Independent events are events where the occurrence of one event does not affect the occurrence of another event. Dependent events are events where the occurrence of one event does affect the occurrence of another event.

5. What is the addition rule of probability?
The addition rule states that the probability of the union of two mutually exclusive events is equal to the sum of their individual probabilities. P(A or B) = P(A) + P(B).

6. What is the multiplication rule of probability?
The multiplication rule states that the probability of the intersection of two independent events is equal to the product of their individual probabilities. P(A and B) = P(A) * P(B).

7. What is conditional probability?
Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted by P(A|B), read as “the probability of A given B.”

8. What is the formula for conditional probability?
The formula for conditional probability is P(A|B) = P(A and B) / P(B).

9. What is the concept of complement in probability?
The complement of an event A, denoted as A’, is the event of all outcomes not belonging to A. The probability of the complement of event A is equal to 1 minus the probability of event A.

10. What is the concept of mutually exclusive events?
Mutually exclusive events are events that cannot occur at the same time. If events A and B are mutually exclusive, then P(A and B) = 0.

11. What is the probability of the union of two mutually exclusive events?
The probability of the union of two mutually exclusive events is equal to the sum of their individual probabilities. P(A or B) = P(A) + P(B).

12. What is the concept of exhaustive events?
Exhaustive events are events that cover all possible outcomes. If events A and B are exhaustive, then P(A or B) = 1.

13. What is the concept of equally likely outcomes?
Equally likely outcomes are outcomes that have an equal chance of occurring. If all outcomes are equally likely, the probability of an event A is P(A) = Number of favorable outcomes / Total number of outcomes.

14. How do you calculate the probability of the intersection of two dependent events?
To calculate the probability of the intersection of two dependent events A and B, you multiply the probability of event A by the probability of event B given event A. P(A and B) = P(A) * P(B|A).

15. What is the difference between permutation and combination?
Permutation refers to the arrangements of objects where the order matters. Combination refers to the selections of objects where the order does not matter.

16. What is the formula for permutation?
The formula for permutation is P(n, r) = n! / (n – r)!, where n is the total number of objects and r is the number of objects to be selected.

17. What is the formula for combination?
The formula for combination is C(n, r) = n! / (r!(n – r)!), where n is the total number of objects and r is the number of objects to be selected.

18. What are the properties of probability?
The properties of probability include: 1) 0 ≤ P(A) ≤ 1, 2) P(S) = 1, where S is the sample space, and 3) P(A’) = 1 – P(A), where A’ is the complement of event A.

19. What is the concept of expected value?
Expected value is the sum of all possible values of a random variable multiplied by their respective probabilities. It represents the long-term average value of an experiment.

20. What is the law of large numbers?
The law of large numbers states that as the number of trials in a probability experiment increases, the experimental probability of an event approaches its theoretical probability.

1. What is the difference between probability and statistics?
Probability deals with the likelihood of events occurring, while statistics involves collecting, analyzing, interpreting, and presenting data.

2. What is a conditional probability?
Conditional probability is the probability of an event occurring, given that another event has already occurred.

3. Explain the concept of Bayes’ theorem.
Bayes’ theorem is a mathematical formula used to calculate the probability of an event occurring, given prior knowledge of related events.

4. What is a random variable?
A random variable is a variable that can take on different values in a probability experiment.

5. What is the difference between discrete and continuous random variables?
Discrete random variables can only take on a finite or countable number of values, while continuous random variables can take on any value within a specified range.

6. Define joint probability.
Joint probability is the probability of two or more events occurring simultaneously.

7. What is the law of large numbers?
The law of large numbers states that as the number of trials in a probability experiment increases, the experimental probability of an event will converge towards its theoretical probability.

8. Explain the concept of expected value.
Expected value is the average value obtained from a probability experiment after repeating it numerous times.

9. What is a probability distribution?
A probability distribution is a table, graph, or formula that describes the likelihood of different outcomes in a probability experiment.

10. What is the difference between mutually exclusive and independent events?
Mutually exclusive events cannot occur at the same time, while independent events are not influenced by the occurrence or non-occurrence of other events.

11. What does the term ‘standard deviation’ represent?
The standard deviation measures the amount of variability or dispersion in a set of data.

12. What is the Central Limit Theorem?
The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size increases.

13. Define confidence interval.
A confidence interval is a range of values within which a population parameter is estimated to fall with a specified level of confidence.

14. What is the difference between Type I and Type II errors?
Type I error occurs when the null hypothesis is rejected when it is actually true, while Type II error occurs when the null hypothesis is accepted when it is actually false.

15. What is a sampling distribution?
A sampling distribution is a probability distribution of a statistic obtained from a large number of samples taken from the same population.

16. Explain the concept of hypothesis testing.
Hypothesis testing is a statistical process used to make inferences about a population based on a sample.

17. What is the likelihood function?
The likelihood function represents the probability of obtaining a particular set of observed data values given a set of parameter values.

18. What is the law of total probability?
The law of total probability states that the probability of an event can be calculated by considering all possible outcomes and their associated probabilities.

19. How is covariance different from correlation?
Covariance measures the relationship between two random variables, while correlation measures the strength and direction of the linear relationship between two variables.

20. Explain the concept of Markov Chains.
Markov Chains are a mathematical model used to describe a sequence of events where the probability of each event depends only on the state attained in the previous event.