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

The video tutorial explains the concept of conditional probability using a biased die example. It derives the probability of events A and B, and explains how to calculate the probability of A given B. The tutorial introduces the formula for conditional probability and discusses its significance, including its application in the Bayes classifier. The video concludes with a brief overview of the next steps in understanding conditional probability.

What was the main characteristic of the die used in the problem?

• Odd faces were twice as likely as even faces.

• All faces were equally likely.

• Even faces were twice as likely as odd faces.

• It had eight faces.

What does the video suggest about the relationship between events A and B?

• A and B are identical.

• A and B are mutually exclusive.

• A is dependent on B.

• A is independent of B.

Why is it necessary to normalize probabilities when considering event B as the sample space?

• To ensure B has a zero probability.

• To increase the probability of A.

• To make A independent of B.

• To treat B as the new sample space.

What is the probability of the intersection of events A and B in the example?

• 6/9

• 1/3

• 2/3

• 4/9

What is the formula for conditional probability?

• Probability of A intersection B divided by probability of B.

• Probability of A divided by probability of B.

• Probability of A times probability of B.

• Probability of A plus probability of B.

What is a key requirement for the conditional probability formula to hold?

• Event B must be less than event A.

• Event A must be greater than event B.

• Event B must have a non-zero probability.

• Event A must be zero.

How does the conditional probability formula relate to the Bayes classifier?

• It is unrelated to the Bayes classifier.

• It forms the basis of the Bayes classifier.

• It contradicts the Bayes classifier.

• It simplifies the Bayes classifier.