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

The video tutorial explains the concept of conditional independence using a coin experiment. Two coins are in a box: one fair and one fake with heads on both sides. Events A and B are defined as the outcomes of two coin tosses, and event C is picking the fair coin. The tutorial calculates the probabilities of these events and demonstrates that A and B are conditionally independent given C, but not independent without this condition. The video provides a detailed walkthrough of probability calculations to illustrate these concepts.

What is the probability of getting heads when tossing a fair coin?

• 1

• 1/2

• 0

• 1/4

What does event C represent in the context of the coin experiment?

• Getting tails on the second toss

• Getting heads on the first toss

• Picking the fake coin

• Picking the fair coin

What is the probability of event A occurring without any conditions?

• 1/2

• 3/4

• 1/4

• 5/8

What is the probability of both tosses resulting in heads if the fake coin is chosen?

• 1/4

• 1/2

• 1

• 3/4

What is the probability of event B occurring without any conditions?

• 5/8

• 1/4

• 3/4

• 1/2

How do events A and B behave when conditioned on event C?

• They have no relation

• They become mutually exclusive

• They become independent

• They remain dependent

What is the probability of both events A and B occurring without conditioning on C?

• 9/16

• 1/4

• 5/8

• 3/4