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

The video tutorial explains the concept of sample space and event complement in probability. It discusses how the probability of an event and its complement add up to one. The tutorial also covers the probability of the union of two events, highlighting the need to subtract the intersection to avoid overcounting. It further explores properties derived from probability axioms, such as the relationship between subsets and their probabilities. The video concludes with a promise of worked examples in the next session.

What is the probability of the complement of an event if the probability of the event itself is 0.3?

• 0.5

• 1.3

• 0.7

• 0.3

What is the result when you apply the probability law to the union of an event and its complement?

• Probability of the event

• Probability of the complement

• 0

• 1

If two events A and B are within a sample space, what is the probability of their union if their intersection is counted twice?

• Probability of Intersection

• Probability of A + Probability of B - Probability of Intersection

• Probability of A - Probability of B

• Probability of A + Probability of B

When two events are disjoint, what is the probability of their intersection?

• 1

• Probability of B

• Probability of A

• 0

What happens to the probability of the intersection of two events if they are not disjoint?

• It is counted twice

• It is added twice

• It is zero

• It is subtracted once

If event A is a subset of event B, how does the probability of A compare to the probability of B?

• Probability of A is less than Probability of B

• Probability of A is less than or equal to Probability of B

• Probability of A is equal to Probability of B

• Probability of A is greater than Probability of B

Which of the following is a consequence of the probability axioms?

• Probability of an event is always greater than 1

• Probability of a subset is less than or equal to the probability of the set

• Probability of a subset is equal to the probability of the set

• Probability of a subset is always greater than the probability of the set