Course Content
Probability Theory Basics
4. Commonly Used Continuous Distributions
5. Covariance and Correlation
Probability Theory Basics
Independence and Incompatibility of Random Events
In probability theory, independence and incompatibility are concepts related to the relationship between random events.
- Independence: Two events are considered independent if the occurrence or non-occurrence of one event does not affect the probability of the occurrence or non-occurrence of the other event. In other words, knowing whether one event happens provides no information about the likelihood of the other event happening.
Events A and B are independent if P(A intersection B) = P(A)*P(B). - Incompatibility: Two events are incompatible if they cannot occur simultaneously. If the occurrence of one event excludes the possibility of the other event happening, they are considered incompatible. For example, flipping a coin and getting heads and tails simultaneously is incompatible since the coin can only show one side at a time.
Events A and B are incompatible if P(A intersection B) = 0.
Examples of independent and incompatible events:
Independant events | Incompatible events |
Results of flipping a fair coin and rolling a fair die | Rolling a die and getting an odd number and an even number on the same roll |
Results of flipping two different coins | Selecting a card from a deck and getting a red card and a black card at the same time |
You draw a card from a standard deck with replacement (after we have drawn a card, we return it back to the deck) . What is the probability of drawing a red card (heart or diamond) followed by drawing a black card (spade or club)?
Select the correct answer
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Section 1. Chapter 5