Probability Rules
Basic Probability Rules (AND, OR, GIVEN)
Learning Objectives
Understand the ‘AND’, ‘OR’ and ‘Given’ probability rules
AND (∩)
- Also known as the intersection
- The ‘overlap’ between two groups or events.
- [latex]P(A \text{ and } B) = P(A|B) \times P(B) = P(B|A) \times P(A)[/latex]
- It does not matter which event, A or B, ‘occurred’ first: [latex]P(A \text{ and } B)= P(B \text{ and } A)[/latex]
OR (∪)
- Also known as the union
- Includes all of both groups or events
- [latex]P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)[/latex]
- It does not matter which event, A or B, ‘occurred’ first: [latex]P(A \text{ or } B)= P(B \text{ or } A)[/latex]
Given (|)
- Also known as a conditional probability
- Is the odds of one event occurring given that another event has already occurred
- The odds of ‘A’ occurring given that ‘B’ has already occurred: [latex]P(A | B) = \frac{P(A \text{ and } B)}{P(B)}[/latex]
- The odds of ‘B’ occurring given that ‘A’ has already occurred: [latex]P(B | A) = \frac{P(A \text{ and } B)}{P(A)}[/latex]
- The order of the events, A or B, matters: [latex]P(B | A) \neq P(A | B)[/latex]
A First BasiC Example
Example 15.1
Problem Setup: Let P(A) = 0.80, P(B) = 0.70, P(A|B) = 0.25
Questions: Can you solve for the following probabilities? And can you find the issue?
- P(A and B)
- P(A or B)
- P(not A)
- P(not B)
Solutions: Click here to download the written solutions. Click below to reveal the answers one at a time. Also see the next section for video solutions.
A second basic example
Example 15.2
Problem Setup: Let P(A) = 0.50, P(B) = 0.60, P(A and B) = 0.25
Questions: Can you solve for the following probabilities?
- P(A | B)
- P(B | A)
- P(A or B)
- P(not B)
Solution: Click here to download the written solutions. Click below to reveal the answers one at a time. Also see the next section for video solutions.
Video Walkthrough of TWO BasiC ExampleS
Key Takeaways (EXERCISE)
Key Takeaways: Basic Probability Rules (AND, OR, GIVEN)
Your Own Notes (EXERCISE)
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