Data Science and Machine Learning (Theory and Projects) A to Z - Probability Model: Probability Models Independence

The video tutorial explains the concept of statistical independence in probability theory. It discusses how two events are considered independent if the occurrence of one does not affect the likelihood of the other. The tutorial also explores conditional probability and poses a question about mutual independence. Additionally, it covers the independence of more than two events, emphasizing the need to establish independence among all subsets of events.

What does it mean for two events to be statistically independent?

• The occurrence of one event affects the likelihood of the other.

• Both events occur simultaneously.

• The occurrence of one event does not affect the likelihood of the other.

• One event is a subset of the other.

If event A is independent of event B, does it automatically mean that event B is independent of event A?

• It depends on the probability values.

• Yes, independence is always mutual.

• No, independence is not necessarily mutual.

• Only if both events have the same probability.

If the probability of A given B is equal to the probability of A, what does this imply?

• A is dependent on B

• A is independent of B

• B is dependent on A

• B is independent of A

What is the formula for the probability of the intersection of two independent events A and B?

• Probability of A plus probability of B

• Probability of A minus probability of B

• Probability of A multiplied by probability of B

• Probability of A divided by probability of B

When considering more than two events, what must be verified to establish their independence?

• The sum of probabilities of all events

• Independence of every subset of events

• The difference in probabilities of all events

• Only the overall probability of all events

What is required to conclude that three events A, B, and C are independent?

• Independence of every possible subset of A, B, and C

• Independence of A, B, and C individually

• The sum of probabilities of A, B, and C

• Only the probability of A intersection B intersection C

What must be true for the formula of independence to hold for more than two events?

• The formula must hold for every subset of events.

• The formula must hold for each individual event.

• The formula must hold for the overall set of events only.

• The formula must hold for the sum of probabilities.