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

The video tutorial introduces conditional probability, explaining standard notations and defining events A and B within a sample space of a die roll. It discusses a loaded die where even numbers are twice as likely as odd numbers, and calculates the probability of event A. The tutorial explores conditional probability, finding the probability of A given B, and concludes with a discussion on the independence of events A and B.

What is the sample space defined in the video?

• 1, 3, 5

• 2, 4, 6

• 1, 2, 3, 4

• 1, 2, 3, 4, 5, 6

How are the probabilities of even numbers compared to odd numbers in the loaded die?

• Even numbers are three times as likely as odd numbers.

• Even numbers are equally likely as odd numbers.

• Even numbers are twice as likely as odd numbers.

• Even numbers are half as likely as odd numbers.

What is the probability of an odd number appearing on the loaded die?

• 3/9

• 4/9

• 2/9

• 1/9

What is the probability of an even number appearing on the loaded die?

• 1/9

• 2/9

• 3/9

• 4/9

What is the probability of event A, where the outcome is not larger than four?

• 6/9

• 4/9

• 2/3

• 1/3

What is the significance of the additivity axiom in probability?

• It allows for the addition of probabilities of mutually exclusive events.

• It allows for the division of probabilities.

• It allows for the multiplication of probabilities.

• It allows for the subtraction of probabilities.

What happens to the sample space when it is known that event B will occur?

• The sample space remains the same.

• The sample space becomes empty.

• The sample space becomes only the outcomes of event B.

• The sample space becomes only the outcomes of event A.

What is the probability of event A given that event B occurs?

• 1/3

• 2/3

• 1/2

• 3/4

What does it mean if the probability of event A does not change given event B?

• Events A and B are independent.

• Events A and B are dependent.

• Event A is impossible.

• Event B is impossible.

What is the mathematical notation for conditional probability?

• P(A * B)

• P(A - B)

• P(A + B)

• P(A | B)