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

The video tutorial covers the three main axioms of probability: non-negativity, additivity, and the probability of the sample space being one. It explains how these axioms form the foundation for understanding probability, using examples like rolling a fair die to illustrate concepts. The tutorial also discusses the probability range between 0 and 1, and derives properties such as the probability of an empty set being zero.

What is the first axiom of probability?

• Probability of any event is always one.

• Probability of any event is a negative number.

• Probability of any event is a non-negative number.

• Probability of any event is always zero.

What does the additivity axiom state about disjoint events?

• The probability of their union is the difference of their probabilities.

• The probability of their union is the division of their probabilities.

• The probability of their union is the sum of their probabilities.

• The probability of their union is the product of their probabilities.

What does it mean for events to be mutually exclusive?

• They never occur together.

• They always occur together.

• They have no intersection.

• They have a common intersection.

According to the third axiom, what is the probability of the entire sample space?

• 0

• It depends on the experiment.

• 1

• 0.5

Why must the probability of any event be between 0 and 1?

• Because probabilities are always zero.

• Because the sample space is exhaustive and has a probability of 1.

• Because probabilities can be negative.

• Because probabilities can exceed 1.

In a fair die example, what is the probability of rolling a 3?

• 1/3

• 1/2

• 1/4

• 1/6

If a die is fair, what is the probability of rolling an even number?

• 1/3

• 2/3

• 1/2

• 1/4

How can the probability of any event be calculated if it is a union of disjoint events?

• By multiplying the probabilities of the outcomes.

• By dividing the probabilities of the outcomes.

• By adding the probabilities of the outcomes.

• By subtracting the probabilities of the outcomes.

What is the probability of the empty set?

• 1

• 0

• It depends on the sample space.

• It is always 0.5.

Why is the probability of the empty set zero?

• Because it is not part of the sample space.

• Because it is part of the sample space.

• Because it has a probability of 1.

• Because it is always 0.5.