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Probability Rules/Non-Disjoint Events and Conditional Probability

Probability Rules/Non-Disjoint Events and Conditional Probability

Author: Al Greene

• Define what it means for events to be disjoint (mutually exclusive)
• Define conditional probability
• Present the rules of probability for non-disjoint events and conditional probability, providing examples of each
• Demonstrate how to represent probability with venn diagrams

This packet shows you what it means to be non-disjoint. We also talk about conditional probability of non-disjoint events. These are very easily demonstrated with Venn diagrams, which we will use. We also have a very Minnesotan example to illustrate the probability formulas.

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What's in this packet

This packet has two videos. The first video shows you the definitions for non-disjoint events and conditional probability, as well as the probability rules for each. The second video shows an example for calculating both non-disjoint event probabilities and conditional probabilities. Some terms that may be new are:

  • The General Addition Rule
  • Conditional Probability
  • The General Multiplication Rule
  • With Replacement versus Without Replacement

Source: Greene


Here are some basic definitions for this packet:

General Addition Rule: The probability of one or both of a pair of events happening is equal to the sum of their individual probabilities minus the probability of both of them happening. This applies to events that are not disjoint. 

Formula: P(A or B) = P(A) + P(B) - P(A and B)


Conditional probability: The probability of an event A happening given the fact that event B already has happened is equal to the probability of both A and B happening divided by the probability of B happening.

Formula: P(A|B) = P(A and B)/P(B)

Source: Greene

Non-Disjoint Events and Conditional Probability- definintions

This video gives you the definitions of non-disjoint events and conditional probability.

Source: Greene

Probablility and Non-Disjoint Events- Examples

This video has a basic example of probability and non-disjoint events.

Source: Greene